Physics 2420 In-Class Problems: DC Circuits

1. Use the loop method to find current through each resistor in the circuit shown below.

2. Use the loop method to find current through each resistor in the circuit shown below.
   
   

3. Use the branch method to find current through each resistor in the circuit shown below. Find the potential difference between points A and B.

4. Use the branch method to find current through each resistor in the circuit shown below. Find the potential difference between points A and B.

5. Redo question #1 using the superposition principle. 
   
   
6. Redo question #2 using the superposition principle.
7. The coil resistor in an ammeter has a resistance which is 100 times larger than the shunt resistor. The galvanometer reads 10.0 mA when the ammeter is used to measure the current in a simple circuit. Unfortunately, the resistor in the simple circuit has a resistance which is only 5.00 times as large as the shunt resistor. What would be current through the resistor if the ammeter was not in place?
8. In the figure below, C₁ = C₅ = 3.00 mF and C₂ = C₃ = C₄ = 2.00 mF. What is the equivalent capacitance of the circuit? A potential of 600 V is applied across points A and B. What is the charge on each capacitor? What is the energy stored in each capacitor?

9. What is the equivalent capacitance of the circuit shown below? A potential of 24 V is applied across points A and B. What is the charge on each capacitor? What is the energy stored in each capacitor?

10. An electronic flash attachment for a camera produces a flash by using the energy stored in a 750-mF capacitor. Between flashes, the capacitor recharges through a resistor whose resistance is chosen so that the capacitor recharges with a time constant of 3.0 s. Determine the value of the resistance.

 
11. A charged capacitor is connected across a 9600-W resistor and discharges to 1% of its maximum charge in a time of 8.3 s. What is the capacitance of the capacitor?
12. Ideal capacitors have an infinite internal resistance. Real capacitors only have a very large resistance as charges leak from one plate to the other. If a capacitor of 8.0 mF has an internal resistance of 5.0 × 10⁸ Ω, how long does it take for one-half of its original charge to leak away?
13. Three identical capacitors are connected with a resistor in two different ways. When they are connected as in part a of the drawing, the time constant to charge up this circuit is 0.020 s. What is the time constant when they are connected with the same resistor as in part b?

14. In the circuit shown below, ε = 12.0 V, r = 0.500 Ω, R₁ = 5.00 Ω, R₂ = 10.0 Ω, and C = 250 mF. Initially, the switch S is open and there is no charge on the capacitor. (a) At the instant S is closed, determine the current supplied by the battery. ( (b) After the switch has be closed for a long time, determine the current supplied by the battery. (c) What is the voltage drop and charge across the capacitor at this later time? (d) Obtain expressions for the current through each resistor and for the charge on the capacitor as a function of time, that is use Kirchhoff's rules and use MAPLE to solve the system of differential equations. Remember that i = dq/dt. (e) The switch is now reopened, how long does it take for the capacitor to lose 80 % of its charge.

15. The inductors in the circuit shown below are magnetically shielded from one another so that they do not produce flux in one another. Determine the time constant of the circuit. Determine how long it takes the current through the resistor to reach 85 % of its maximum. At this point, what is the energy stored in each inductor?

16. The inductor in the diagram below is ideal with no resistance. (a) Determine the current through the resistors, the instant that the switch S is closed. (b) Determine the currents through the resistors when the switch S has been closed for a long time. (c) Determine the time dependence of the currents. Use Kirchhoff's rules and use MAPLE so solve the resulting system of differential equations. (d) The switch S is now closed. How long will it take for the current to drop to 20 % of its initial value?

Questions? mike.coombes@kwantlen.ca