Physics 1220 In-Class Problems: DC Circuits and Kirchhoff's Rules

1. Give the minimum number of equations to find the current in each branch of the circuit shown below. Find the currents.

   

2. Give the minimum number of equations to find the current in each branch of the circuit shown below. Find the currents.

   

3. Give the minimum number of equations to find the current in each branch of the circuit shown below. Find the currents. Find the potential difference between points A and B

   

4. Give the minimum number of equations to find the current in each branch of the circuit shown below. Find the currents. Find the potential difference between points A and B.
   
   

5. For the circuit shown below give the minimum set of equations that determines the current in each branch. You do not need to solve the system of equations.

   

6. Consider the circuit below. Determine the potential with respect to the negative terminal of the battery at the points A, B, and C labelled on the diagram.

   

7. Consider the circuit below. The potential with respect to the negative terminal of the battery at point B is 6.0 V. Determine the battery voltage ε and the potential at the points A and C labelled on the diagram.


Meters

8. A galvanometer has a coil resistance of 250 Ω and requires a current of 1.5 mA for full-scale deflection. This device is used in an ammeter that has a full-scale deflection of 25.0 mA. What is the value of the shunt resistance?
   

9. Consider the circuit in diagram (a) below. What is the current in this circuit? Now consider the circuit in diagram (b) below. The only difference is that an ammeter has been added so that the current could be measured. The ammeter is the same one as the previous problem. What is the current reading on the ammeter? Why is it different from the theoretical value that you found for diagram (a)?
   

10. 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?
    

11. A galvanometer with a full-scale deflection of 2000 μA has a coil resistance of 100 Ω. If it is to be used as a voltmeter with a full-scale deflection of 1.5 V, what would be the required multiplier resistance?
    

12. Consider the circuit in diagram (a) below. What is the potential difference over the 140 kΩ resistor in this circuit? Now consider the circuit in diagram (b) below. The only difference is that a voltmeter has been added so that the potential difference could be measured. The voltmeter is the same one as the previous problem. What is the voltage reading on the voltmeter? Why is it different from the theoretical value that you found for diagram (a)?
    

RC Circuits

13. An electronic flash attachment for a camera produces a flash by using the energy stored in a 750-μF 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.

14. A charged capacitor is connected across a 9600-Ω resistor and discharges to 1% of its maximum charge in a time of 8.3 s. What is the capacitance of the capacitor?
    

15. 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 μF has an internal resistance of 5.0 × 10⁸ Ω, how long does it take for one-half of its original charge to leak away?
    

16. 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?
    

17. In the circuit shown below, ε = 12.0 V, r = 0.500 Ω, R₁ = 5.00 Ω, R₂= 10.0 Ω, and C = 250 μF. Initially, the switch S is open. (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) The switch is now reopened, how long does it take for the capacitor to lose 80% of its charge.

18. Consider the circuit below. Both capacitors are initially uncharged. Switch S₂ is closed followed by S₁.

    (a)    At that instant what is the conventional current (magnitude and direction) in each resistor?

    (b)   After the switches have been closed for a long time, what is the conventional current (magnitude and direction) in each resistor?

    (c)    Now S₂ (and only S₂) is reopened. At this instant what is the conventional current (magnitude and direction) in each resistor?

    (d)   How long will it take for the current in the 30-Ω resistor to drop to 0.10 A?
    

    

19. When the switch is closed in the circuit below what is the initial current in each resistor? After the switch has been closed for a long time what is the current through each resistor? What is the voltage across the capacitor and its charge at that later time? If the switch S is reopened, what is the current through each resistor? How long will it take for the capacitor to lose 70% of its charge (Hint: what is the equivalent resistance of circuit)?



20. Consider the RC circuits shown below. The voltage drop and its direction for the capacitor are given. Find the current and its direction at the instant the switch S is closed.

Questions? mike.coombes@kwantlen.ca