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.