Capacitance

Impedance

Average Emf

Magnetic Field

What is the current in R₂?

What is the resistance of the combination of resistors?

5. What is the resistance of the combination of resistors?

x₁, x₂, x₃, and x₄ are some numbers.
Answer:

(10³ x₁( x₂+x₃)/(10³ x₁+x₂+x₃) + x₄) Ω

What Voltage is Necessary?

4. To store x₁ mJ of energy in an x₂ μF capacitor, what voltage is necessary?
x₁ and x₂ are some numbers.

Solution:
U = x₁ mJ = x₁ ∙ 10⁻³J
C = x₂ μF = x₂∙ 10⁻⁶ F
V²= 2U/C = 2x₁ ∙ 10⁻³J/(x₂∙ 10⁻⁶ F) = 2∙ 10³x₁/x₂ J/F
V=(2∙10³ x₁/x₂)⁰·⁵ V = 44.7(x₁/x₂)⁰∙⁵ V

Helium Nucleus is Accelerated

3. A helium nucleus is accelerated from rest through a potential difference V to a kinetic energy of X ∙ 10⁻¹³ J. What is the potential difference V? X is some number. Answer: V = E/q = E/(2e) = X ∙ 10⁻¹³ J / (2∙1.60×10⁻¹⁹ C) =  0.312X MV

What is the potential difference V?

3. A helium nucleus is accelerated from rest through a potential difference V to a kinetic energy of X ∙ 10⁻¹³ J. 

What is the potential difference V?
X is some number.

Answer:

V = E/q = E/(2e) = X ∙ 10⁻¹³ J / (2∙1.60×10⁻¹⁹ C) = 0.312X MV

Three Point Charges

1. Three point charges are positioned as follows: q₁ is at (x₁ m, y₂ m), q₂ is at (x₂ m, y₂ m), and q₃ is at (x₂ m, y₃ m). If q₁ = b₁ μC, q₂ = b₂ μC, and q₃ = b₃ μC, what is the magnitude of the force on q₂?

x₁, y₂, x₂, y₃, b₁, b₂, and b₃ are some numbers.

Answer:

|F(q₂)| = kq₂ ( (q₁/r₁²)²+(q₃/r₃²)² )⁰·⁵ =
= 8.99·10⁻³ ( (b₁/(x₂-x₁)²)²+(b₃/(y₃-y₂)²)² )⁰·⁵ N

General Physics II: Algebra Based PHYS 1434 (course) Final Examination

New York City College of Technology
The City University of New York
General Physics II: Algebra Based PHYS 1434 (course) Prof. Vasiliy Znamenskiy
Final Examination December 15-21, 2015

(PDF) | (RTF)

1. Three point charges are positioned as follows: q₁ is at (x₁ m, y₂ m), q₂ is at (x₂ m, y₂ m), and q₃ is at (x₂ m, y₃ m). If q₁ = b₁ µC, q₂ = b₂ µC, and q₃ = b₃ µC, what is the magnitude of the force on q₂?
x₁, y₂, x₂, y₃, b₁, b₂, and b₃ are some numbers.

2. A thin spherical shell of radius x₁ cm has x₂ µC of charge uniformly distributed over its surface. What is the electric flux through an area of x₃ m2 of a spherical surface concentric with the shell of charge but having a radius of x₄ m?
x₁, x₂, x₃, and x₄ are some numbers.

3. A helium nucleus is accelerated from rest through a potential difference V to a kinetic energy of x₁  10-13 J. What is V? x₁ is some number.

4. To store x₁ mJ of energy in an x₂ F capacitor, what voltage is necessary?
x₁ and x₂ are some numbers.


5. What is the resistance of the combination of resistors?


x₁, x₂, x₃, and x₄ are some numbers.


6. If R₁ = x₁ , R₂ = x₂ , R₃ = x₃ , ₁ = x₄ V, and ₂ = x₅ V, what is the current in R₂?

x₁, x₂, x₃, and x₄ are some numbers.

7. Two parallel wires run in a north-south direction. The eastern wire carries x₁ mA southward while the western wire carries x₂ mA northward. If the wires are separated by x₃ cm, what is the magnitude and the direction of the magnetic field at a point between the wires at a distance of x₄ cm from the western wire?

x₁, x₂, x₃, and x₄ are some numbers.

8. A N turn coil of area x₁ cm2 is placed in a magnetic field so that the normal to its area is in the direction of the field. If the field originally has a value of x₂ T that increases to x₃ T in x₄ ms, what is the average emf induced in the coil? x₁, x₂, x₃, and x₄ are some numbers.

9. A series RLC circuit has a resistance of x₁ k, and inductance of x₂ mH, and a capacitance of x₃ F. The power source provides a voltage of v = x₅ V· sin(x₆ rad/s·t). What is the impedance of this circuit? x₁, x₂, x₃, x₄, x₅, and x₆ are some numbers.

10. An RLC series circuit has a 25 k resistor, a 4.0 H inductor, and a capacitor. What capacitance would result in resonance at 15 kHz?

11. If the rms value of the electric field is x₁ V/m at a distance of x₂ m from an isotropic point source, what is the rms value of the magnetic field at a distance of x₃ m from the source? x₁, x₂, and x₃ are some numbers.

12. In order to produce an image double the size of an object with a converging lens of focal length f, what object distance should be used? Construct the rays diagram in order to show the general location, size, orientation, and type of image formed by the lens.

13. Laser light of x₁ nm wavelength is shown through parallel slits forming a series of maxima on a screen x₂ m away. If the distance between the central maximum and the first order maximum is x₃ cm, what is the slit separation? x₁, x₂, and x₃ are some numbers.

14. Radioactive particles moving at 0.70 c are measured to have a half-life of 5.2  10-6 s. What is their half-life when at rest?

15. A material X has a work function of 1.23 eV. What is the longest wavelength that could cause photoelectrons to be released from the material X?

Practice Final Exam

Practice Final Exam

1. A thin metallic shell of radius x1 cm has a charge of -x2 nC on it. At the center of the sphere is a point charge of x3 nC. What is the electric field x4 cm from the center of the shell?
2. Three x1 C charges are placed along the x-axis, one charge at x = x2 cm, another at the origin, and the last one at x = x3 cm. What is the total potential energy of this arrangement?
3. A variable resistor has a voltage of x1 V placed across it. If the resistance is increased x2%, what happens to the current through it?

4. A power line carries x1 kA at a height of x2 m above the ground. What is the resulting magnetic field at ground level?

5. Doubling the diameter of a loop of wire produces what change of induced emf?
6. An RLC series circuit has a x1 Ω resistance, a x2 mH inductor, and a capacitor. If the circuit is in resonance at x3 kHz, what is the capacitive reactance?

7. In vacuum, the components of an EM wave are E_y = 50(V/m)cos[(5.00 m^-1)x + π/4], E_x = 0, and E_z = 0. What is the wavelength of the wave?

8. A ray of light enters an equilateral prism made of material with n = x1 at an angle of incidence . The internally refracted ray is parallel to the base of the prism. What is the angle of refraction for the ray leaving the prism?

9. If light of wavelength x1 nm is used in a double-slit experiment with slit separation x2 mm, what angle separates the two 4^th order maxima?

10. Spaceships A and B are moving in the same direction along the same straight line. Spaceship A is moving at 0.800 c relative to a stationary observer, and spaceship B is moving at 0.800 c relative to spaceship A. What does the stationary observer find for the speed of spaceship B?

11. Light of wavelength x1 nm bombards a surface with work function x2 eV. What is the maximum kinetic energy of the photoelectrons from this surface?

giga, mega, kilo, hecto, deca, deci, centi, milli, micro, nano

SI Prefixes #SI #SIPrefix SIPrefixes #prefix #prefixes

A photo posted by Vasiliy S. Znamenskiy (@znamenski) on Dec 5, 2015 at 12:13pm PST

Exam 2 Problem 7 Solution

Exam 2 Problem 6 Solution

6. The difference between the highest and lowest voltage of a household "120 V-emf" is ___


Data 
Vrms = 120 V
vmax – vmin =?

Physics Formulas
Amplitude V=√2 Vrms
Vmax – Vmin = 2V = 2∙Amplitude 

Solution
Vmax  – Vmin  = 2V = 2∙√2 Vrms
Vmax  – Vmin= 2∙√2∙120V= 339V

Exam 2 Problem 5 Solution

Exam 2 Statistics

Exam 2

2015 Fall Term (1) General Physics II: Algebra Based PHYS 1434 D720[31546] (NYC College of Technology)

Magnetic Fields

How Capacitors Store Electrical Energy

Problem. PS and PP are rates of energy dissipation in 3 resistors...

Problem

P_S and P_P are rates of energy dissipation in 3 resistors, when they are connected in series and in parallel respectively with some source of constant voltage. Let lowest resistance is known, r, 2^nd resistance is greater then the first on the factor of N. What is the resistance of the 3^rd resistor?
(a) Derive algebraic expression for the second resistance
and then
(b) use this expression to find numerical solution for the following data:
P_S=1 W, P_P=11 W, N=2, r=1Ω.

Solution:

V²/R_P=P_P

V²/R_S=P_S

R is 3^rd resistance.

R_S=r+Nr+R

1/R_P=1/r+1/(Nr) +1/R

R_P=1/( 1/r+1/(Nr) +1/R  )

P_P/P_S =R_S/R_P = R_S·(1/R_P)

P_P/P_S =R_S/R_P = (r+Nr+R)·( 1/r+1/(Nr) +1/R)

P_P/P_S=a

(r+Nr+R) (1/r+1/(Nr)+/R)=a

(1+N+R/r)(1+ 1/N + r/R) = a; Solve for x=R/r

R/r=x

P_P/P_S=a=11

11=(1+2+x)(1+1/2+1/x)

11=(3+x)(3/2+1/x)

11x=(3+x)(1.5x+1)

Solutions: x=3, x=2/3

R/r = 3

R=3·1Ω = 3Ω

Problem: PS and PP are rates of energy dissipation in two resistors, when they are connected in series and in parallel respectively with some source of constant voltage. Let lower resistance is known, r, what is resistance of another resistor?

Problem

P_S and P_P are rates of energy dissipation in two resistors, when they are connected in series and in parallel respectively with some source of constant voltage. Let lower resistance is known, r, what is resistance of another resistor?
(a) Derive algebraic expression for the second resistance
and then
(b) use this expression to find numerical solution for the following data:
P_S=12 W, P_P=54 W, r=1Ω.

Solution:

V²/R=P

R_S=R+r

1/R_P=1/R+1/r=(R+r) / (Rr)

R_P=Rr/(R+r)

V²/R_P=P_P

V²/R_S=P_S

R_S/R_P=P_P/P_S

(R+r) / (Rr/(R+r)) = (R+r)²/Rr=P_P/P_S=a

(R+r)²/Rr=a

(R+r)²=aRr

(R/r+1)²=aR/r

R/r = x

(x+1)²=ax

x²+2x+1=ax

x²+2x-ax=-1

x²+2(1-a/2)x=-1

x²+2(1-a/2)x+(1-a/2)²=-1+(1-a/2)²

(  x+(1-a/2)  )² = -1+(1-a/2)²

x+(1-a/2) = ± (  -1+(1-a/2)²  )^½

x=-(1-a/2) ± (  -1+(1-a/2)²  )^½

x=(a/2 - 1) ± ( (a/2-1)²-1  )^½

R/r =    (P_P/P_S)/2 – 1) ±  ((P_P/P_S)/2-1)²-1  )^½

R = r·(   (P_P/P_S)/2 - 1) ± ( ((P_P/P_S)/2-1)²-1  )^½ )

(a)        R = r·(   (P_P/P_S)/2 – 1) + ( ((P_P/P_S)/2-1)²-1  )^½ )

(P_P/P_S)/2 - 1) = (54 W/12 W)/2-1

(P_P/P_S)/2 - 1) = (  9 / 2) /2-1 = 9/4 – 4/4 = 5/4

R = 1Ω ·(5/4 + (25/16-1) ^½) = 1Ω ·(5/4 + (25/16-16/16) ^½) = 1Ω ·(5/4 + (9/16) ^½) = 1Ω ·(5/4 + ¾) = 1Ω ·(8/4) =2Ω

(b)  R = 2Ω

What is the resistance...

4. What is the resistance (R) of the resistor if the electric current (I) flowing through this resistor is equal to 2 A, and the electric potential (V_L) on the left terminal of this resistor is 4 V and the electric potential (V_r) on the right terminal of this resistor is 10 V. Which is direction of the electric current through this resistor, toward left or right?
V_r - V_L = ΔV_r,l = -I_r,l R
-I_r,l R = (V_r - V_L )

-I_r,l  = (V_r - V_L )/R

I_r,l  = (V_L – V_r )/R

 R = |(V_L – V_r )/ I_r,l |

R  = |(4V – 10V )/2A| = 3 Ω

The electric current flows from greater potential, 10V, right, to the lower potential, 4V, left: toward to left.

Exam 1. Problem 1

Exam 1. October 8, 2015, 8:00 AM
In solutions students should show:
a) given data by symbols,
b)   the unknown by symbol,
c) useful for this problem general formulae,
d) algebra job and final algebraic expression for the unknown,
e) substitution of symbols in the final algebraic expression by numbers with measurement units,
f) if it is required by a problem the final number with measurement units.

1. Electric field (E) accelerates a charged droplet from the zero speed to the final speed (V₁) of 8 m/s. What will be the final speed (V₂) if the electric field is decreased by a factor of 4, but all other parameters of this accelerator are not changed?

The electric field is decreased by a factor of 4 means: E₂= E/4, E₂/E=1/4

Potential energy of electric field, U=E∙d∙q
Kinetik Energy, K=½mv²

U=K

E∙d∙q = ½mv₁²,
where d is the traveling distance of the droplet in the electric field, q is the droplet’s electric charge.

E₂∙d∙q = ½mv₂²

(E₂∙d∙q)/ (E₁∙d∙q) =  (½mv₂²)/(½mv₁²)

E₂/ E =  v₂²/v₁²

v₂² = v₁² ∙E₂/ E

v₂ = v₁ ∙(E₂/ E)^1/2

v₂ = 8m/s ∙(1/4)^1/2 = 8m/s ∙(1/2) = 8m/s  /2 = 4m/s   

Practice Problems for the Exam 1.

 1. W_S is the rate of the energy dissipation in two resistors with resistances R₁ and R₂, when they are connected in series with a source of constant voltage. What is the rate of the energy dissipation in these two resistors when they and the source of constant voltage are connected in parallel?

2. W_S is the energy dissipation in 3 resistors, when they are connected in series with some source of constant voltage. Resistances are R₁, R₂, and R₃. What is the energy dissipation in these 3 resistors, when they are connected in parallel (W_P)?

3. R₁ and R₂ are resistances of two pieces of wire. The wires have different cross-sectional areas, and the length of the second wire is greater by the factor of N than the length of the first wire. The wires made from the same material. What is the ratio of m₁/m₂, where m₁ and m₂ are masses of these resistors? Derive algebraic expression for ratio m₁/m₂ in terms of R₁, R₂, and N.

4. A positive charge, Q₁, is located in the coordinates (x₁, y₁, z₁). Negative charge, -Q₂, is located in coordinates (x₂, y₂, z₂). Q₁ > Q₂. What are coordinates of a point on the straight line passing through the first and the second charge, where the electric field, created by these two charges, is equal to zero? Find algebraic expression in the terms of x₁, y₁, z₁, x₂, y₂, z₂, Q₁, and Q₂.

5. Two equivalent electric charges repel each other with the force F_I. What will be the interaction force F_F, if P% of one charge is transferred to the other?

6. U_S is total energy of two capacitors with capacitance C₁ and C₂, when they are connected in series with a source of constant voltage. What is total energy of these two capacitors, when they and the source of constant voltage are connected in parallel?

7. What is ratio of R_S/R_P for the N identical resistors, where R_S and R_P are their equivalent resistances when they are connected in series and in parallel respectively?

8. A positive charge Q₁ is located on the distance d₁ from some point in space. What is the distance (d₂) between the same point in space and the negative charge -Q₂, if the electric potentials of electric field, created by these two charges in this point and on the very far distance from these two charges are equal each other? 

9. An electric current I flows through a resistor with the resistance R from the resistor's terminal A to the terminal B. The electric potential in the point A is equal to V_A. What is the electric potential in the point B?

10. A capacitor with the capacitance C and the initial potential V totally discharges through some resistor and produces average current I in this resistor. What is the time of this discharge?

11. Five electric charges 10C, 11C, 12C, 13C, 14C are located on the X axis in coordinates 1m, 2m, 3m, 4m, and 5m respectively. There is a sphere with radius 1.1 m and which the center located in one of these electric charges. If the flux of the electric field, created by these electric charges, flowing through the surface of this sphere, equal to 39C/ε₀ ,  what is the coordinate of the sphere center? 

ε₀ = 8.9 × 10⁻¹² F/m

12. Two identical positive electric charges Q repel each other with the force F_I. When additional electric charge is added in the middle point between these two electric charges, magnitudes of net forces acting to old charges are F_F. Derive expression for additional electric charge in the terms of Q, F_I, F_F.

 13. Electric field E in an accelerator accelerates a charged droplet from the zero speed to the final speed V₁. To increase the final speed to V₂ electric field have to be increased by the factor of N. Derive expression for the factor N in terms of V₁ and V₂.

14. If the charge Q₁ is located on the vertex of acute angle of right triangle oppositely to the cathetus with the length d₁, and the charge Q₂ is located on the vertex of the acute angle, opposite to cathetus with the length d₂, then the net force F acts to the charge Q₃ located on the vertex of the right angle. Find algebraic expression for the magnitude of force F in terms of Q₁, Q₂, Q₃, d₁, and d₂.

Derive Algebraic Expressions. Parallel and Series Resistors.

1. Four resistors R₁, R₂, R₃, and R₄ are connected in parallel. A drop of the electric potential on the resistor R₁ is V₁. Derive an algebraic expression for the drop of the electric potential on the resistor R₄ in the terms of R₁, R₂, R₃, R₄, and V₁.

2. Four resistors R₁, R₂, R₃, and R₄ are connected in series. An electric current through the resistor R₁ is I₁. Derive an algebraic expression for the electric current through the resistor R₄ in the terms of R₁, R₂, R₃, R₄, and I₁.

3. Four resistors R₁, R₂, R₃, and R₄ are connected in series. A drop of the electric potential on the resistor R₁ is V₁. Derive an algebraic expression for the drop of the electric potential on the resistor R₄ in the terms of R₁, R₂, R₃, R₄, and V₁.

4. Four resistors R₁, R₂, R₃, and R₄ are connected in parallel. An electric current through the resistor R₁ is I₁. Derive an algebraic expression for the electric current through the resistor R₄ in the terms of R₁, R₂, R₃, R₄, and I₁.

5. Four resistors with known resistances R₁, R₂, R₃, and unknown R₄ are connected in series. An equivalent resistance is R. Derive an algebraic expression for the unknown resistance R₄ in the terms of known parameters. 

6. Four resistors with known resistances R₁, R₂, R₃, and unknown R₄ are connected in parallel. An equivalent resistance is R. Derive an algebraic expression for the unknown resistance R₄ in the terms of known parameters. 

7. Four resistors with known resistances R₁, R₂, R₃, and unknown R₄ are connected in series to a battery with a known terminal voltage V. The total power P of electric energy being dissipated in all resistors is known. Derive an algebraic expression for the unknown resistance R₄ in the terms of known parameters. 

8. Four resistors with known resistances R₁, R₂, R₃, and unknown R₄ are connected in parallel to a battery with a known terminal voltage V. The total power P of electric energy being dissipated in all resistors is known. Derive an algebraic expression for the unknown resistance R₄ in the terms of known parameters. 

When a series combination of two uncharged capacitors is connected to a 12 V battery

5.  When a series combination of two uncharged capacitors is connected to a 12 V battery, 96 mJ of energy is drawn from the battery.  If one of the capacitors has a capacitance of 4 mF, what is the capacitance of the other?

1. Algebra Based Solution

Given Data: Vb=12V U=96 mJ C1=4mF C1 and C2 are series C2=?

Useful formulas: U=QV/2=CV2/2 C=Q/V 1/Ceq=1/C1+1/C2

Algebra Job U=CeqVb2/2 1/Ceq= Vb2/(2U) 1/C1+1/C2 = Vb2/(2U) 1/C2 = Vb2/(2U) - 1/C1 C2=1/( Vb2/(2U) - 1/C1 ) or 1/C2 = Vb2/(2U) - 1/C1 1/C2 = (Vb2/2 – U/C1) /U C2 = U/(Vb2/2 - U/C1)

Substitution and Calculation:

C₂=1/( V_b²/(2U) - 1/C₁ ) = 1/(  (12V)²/(2·96 mJ) - 1/(4mF)  )

Expression for Google Scientific Calculator

1/( (12Volt)^2/(2*96microjoule) – 1/(4microfarad)) in microfarad

Google result: 2 microfarad

Result: C₂ = 2mF

2. Arithmetic Based Solution

Given Data: Vb=12V U=96 mJ C1=4mF C1 and C2 are series C2=?

Useful formulas: U=QV/2=CV2/2 C=Q/V 1/Ceq=1/C1+1/C2

U=CeqVb2/2 96mJ =Ceq(12V)2/2 (4·4·2·3)mJ =Ceq ·4·3·4·3V2/2 (2)mJ =Ceq ·3V2/2 4/3 (mJ/ V2) = 4/3 mF = Ceq 1/Ceq = ¾  · 1/mF 1/C2=1/Ceq-1/C1 1/C2 = ¾ · 1/mF – ¼ ·1/mF 1/C2 = 2/4 · 1/mF = 1/2  · 1/mF C2= 2mF

3. Another Arithmetic Based Solution

Given Data: Vb=12V U=96 mJ C1=4mF C1 and C2 are series C2=?

Useful formulas: U=QV/2=CV2/2 C=Q/V Q1=Q2=Qeq=Q Vb=V1+ V2

Q=2U/V=2·96 mJ/12V Q= 2·4·4·2·3 /(4·3) mJ/V   Q= 2·4·2 mC V1=Q/C1=2·4·2 mC/4mF=4V V2=Vb -V1=12V-4V=8V C2=Q/V2=2·4·2 mC/8V=2mF C2= 2mF

Homework Quiz 5. Resistance-Capacitance Circuits

1. A series circuit consists of a 1.02 V source of emf, a 2.00 mF capacitor, a 1000 W resistor, and a switch. When the switch is closed, how long does it take for the current to reach one-half its maximum value? 
A. 0.693 s                              B. 1.69 s                C. 0.0250 s                            D. 2.00 s                E. 1.39 s

2.  The ammeter your physics instructor uses for in-class demonstrations has a resistance R_g and requires a current of 1.0 mA for full-scale deflection. The same ammeter can be used to measure currents of much greater values by wiring a shunt resistor of relatively small resistance, R_p , in parallel with the ammeter. The shunt resistance needed to produce a full-scale current of 12 A is 3.5 mW.  What is the resistance of the ammeter, R_g?  
A.  75 W.                         B.  28 W.                              C.  35 W.                             D.  42 W.                             E.  60 W.

3. Two identical circuits have a capacitor in series with a resistor.  In circuit A, the resistor has resistance R, while in circuit B, its resistance is 4R.  The capacitors are identical.  Each capacitor begins fully charged, and each circuit is open.  When each circuit is connected (i.e. the switch in them is closed) the capacitor will fully discharge.  If a time t is required for circuit A’s capacitor to fully discharge, what time will be required for circuit B’s capacitor to do the same?  
A. 0.5t                    B. 2t                       C. 4t                       D. t                          E. 0.25t
4. In the circuit shown, with the switch open the capacitor is completely uncharged. The switch is closed for a long time. the current through the circuit is 0.2 A. Determine the value of the unknown resistor.

A. 61 W              B. 70 W              C. 27 W              D. 10 W              E. 56 W  

5.  A galvanometer reads I = 6 mA full scale and has an internal resistance r = 9.1 ohms. If a resistor, R = 425 W is connected in series with the galvanometer, what is the full scale voltage of the device?

A.  2.55 V                       B.  7.15 V                              C.  7.10 V                              D.  4.23 V                             E.  2.60 V

6. A capacitor is connected in series with a resistor and a switch. With the switch open, the capacitor is charged to 9.0 V. When the switch is closed, how long will it take for the voltage across the capacitor to drop to 6.0 V if the time constant of the circuit is 4.0 s? 
A. 2.7 s                   B. 1.6 s                   C. 12 s                    D. 1.2 s                   E. 0.3 s

7. In an RC circuit with an initially uncharged capacitor, the time constant is the time that is required for the charge on the capacitor to reach what percentage of its final value?
A. 100%                B. 63%                   C. 37%                   D. 50%                   E. 90%                    

8. In the circuit shown in the figure, the switches S1 and S2 are initially open and the 20-mF capacitor has a charge of 100 mC. About how long will it take after switch S1 is closed (switch S2 remains open) for the charge on the capacitor to drop to 5 mC?

A. 3.0 s                   B. 9.0 s                   C. 6.0 s                   D. 18 s                    E. 12 s                   9.  A series circuit consists of a 12.0 V source of emf, a 2.00 mF capacitor, a 1000 W resistor, and a switch. What is the time constant for this circuit?  
A.  10.0 s                             B.  0.693 s                           C.  0.0825 s                         D.  1.00 ms                         E.  2.00 s  

10.  A 9.0000-V battery is used to produce a current through two identical resistors in series, each having a resistance of 150.00 kW. A handheld digital multimeter (DMM) is used to measure the potential difference across the first resistor by placing probe leads at each end of this resistor. Typical DMMs have an internal resistance of 10 MW. What is the current in the circuit with the DMM connected?  
A.  30.33 mA                    B.  30.00 mA                    C.  29.78 mA                    D.  30.14 mA                    E.  30.22 mA           

11. Two parallel plate capacitors, C₁ and C₂ are connected in series to a 60-V battery, a switch S, and a 200-KW resistor as shown in the figure. Both capacitors are air gap capacitors and have plates with an area of 2.0 cm² and a separation of 0.10 mm. The capacitors are initially uncharged and switch S is open. After switch S is closed, how long will it take for the capacitors to charge to 50% of their maximum value?

A. 1.2 ´ 10^-6 s                   B. 8.9 ´ 10^-7 s                   C. 1.8 ´ 10^-6 s                   D. 2.5 ´ 10^-6 s                   E. 4.9 ´ 10^-6 s 

12. When being used to measure current, an ammeter should be connected in 
A. series with the circuit.       B. series with the voltmeter.     C. parallel with the circuit.    D. parallel with the voltmeter. 

13.  What is the ratio of the time for the capacitor in an RC series circuit to reach 90% of capacity from an empty state, to that for the circuit to discharge from a ‘full’ state to 90% capacity?   
A.  1/9 as long       B.  Answer depends on the particular values of R and C.      C.  The same time is required                      
D.  1/22 times as long                               E.  22 times as long                   F.  9 times as long  

14. In the circuit shown, R₁ = 10 W, R₂ = 4 W, R₃ = 10 W, e = 10 V, and capacitor has a capacitance C = 2 mF. Determine the energy stored in the capacitor when switch S has been closed for a long time.

  A. 4.94 µJ                              B. 3.27 µJ                              C. 3.55 mJ                             D. 1.02 mJ                              

15. In an RC circuit with an initially uncharged capacitor, the time constant is the time that is required for the current through the resistor to reach what percentage of its initial value?  A. 63%               B. 37%              C. 100%             D. 50%        E. 90% 

16. In the figure shown, the time constant for the discharge of the capacitor is

 A. 40 sec.                     B. 20 sec.                        C. 50 sec.                        D. 10 sec.                               E. 30 sec.

17. In a series circuit consisting of a 12.0 emf, a 2.00 mF capacitor, a 1.00 kW resistor and a switch, what is the voltage across the capacitor at a time t after the switch is closed? 
A. 6.32 V                               B. 7.58 V                               C. .632 V                               D. 8.65 V                                

18.  A voltmeter must be placed in parallel with the circuit element whose voltage is to be measured. An ideal voltmeter therefore has  
A.  zero resistance.                               B.  infinite resistance.                          D.  None are correct.  

19. A series circuit consists of a 12.0 V source of emf, a 2.00 mF capacitor, a 1000 W resistor, and a switch. When the switch is closed, how long does it take for the current to reach one-tenth its maximum value? 
A. 4.61 s                B. 0.693 s                              C. 18.0 s                D. 2.30 s                E. 9.00 s 

20.  A capacitor in an RC circuit is charged, storing energy 1.25mJ.  What is the time required to discharge this capacitor, as compared to the time required to discharge an identical capacitor in an identical RC circuit which has stored 2.5mJ?   
A.  twice the time                 B.  the answer depends on the values of R and C.        C.  half the time   D.  the same time