21.1 Resistors in Series and Parallel
The figure above shows a circuit containing two batteries and three identical resistors with resistance R. Which of the following changes to the circuit will result in an increase in the current at point P? Select two answers.
 Reversing the connections to the 14 V battery.
 Removing the 2 V battery and connecting the wires to close the left loop.
 Rearranging the resistors so all three are in series.
 Removing the branch containing resistor Z.
In a circuit, a parallel combination of six 1.6kΩ resistors is connected in series with a parallel combination of four 2.4kΩ resistors. If the source voltage is 24 V, what will be the percentage of total current in one of the 2.4kΩ resistors?
 10%
 12%
 20%
 25%
If the circuit in the previous question is modified by removing some of the 1.6 kΩ resistors, the total current in the circuit is 24 mA. How many resistors were removed?
 1
 2
 3
 4
Two resistors, with resistances R and 2R are connected to a voltage source as shown in this figure. If the power dissipated in R is 10 W, what is the power dissipated in 2R?
 1 W
 2.5 W
 5 W
 10 W
In a circuit, a parallel combination of two 20Ω and one 10Ω resistors is connected in series with a 4Ω resistor. The source voltage is 36 V.
 Find the resistor(s) with the maximum current.
 Find the resistor(s) with the maximum voltage drop.
 Find the power dissipated in each resistor and hence the total power dissipated in all the resistors. Also find the power output of the source. Are they equal or not? Justify your answer.
 Will the answers for questions (a) and (b) differ if a 3 Ω resistor is added in series to the 4 Ω resistor? If yes, repeat the question(s) for the new resistor combination.
 If the values of all the resistors and the source voltage are doubled, what will be the effect on the current?
21.2 Electromotive Force: Terminal Voltage
Suppose there are two voltage sources – Sources A and B – with the same emfs but different internal resistances, i.e., the internal resistance of Source A is lower than Source B. If they both supply the same current in their circuits, which of the following statements is true?
 External resistance in Source A’s circuit is more than Source B’s circuit.
 External resistance in Source A’s circuit is less than Source B’s circuit.
 External resistance in Source A’s circuit is the same as Source B’s circuit.
 The relationship between external resistances in the two circuits can’t be determined.
Calculate the internal resistance of a voltage source if the terminal voltage of the source increases by 1 V when the current supplied decreases by 4 A? Suppose this source is connected in series (in the same direction) to another source with a different voltage but same internal resistance. What will be the total internal resistance? How will the total internal resistance change if the sources are connected in the opposite direction?
21.3 Kirchhoff’s Rules
An experiment was set up with the circuit diagram shown. Assume R_{1} = 10 Ω, R_{2} = R_{3} = 5 Ω, r = 0 Ω and E = 6 V.

One of the steps to examine the setup is to test points with the same potential. Which of the following points can be tested?
 Points b, c and d.
 Points d, e and f.
 Points f, h and j.
 Points a, h and i.
At which three points should the currents be measured so that Kirchhoff’s junction rule can be directly confirmed?
 Points b, c and d.
 Points d, e and f.
 Points f, h and j.
 Points a, h and i.

If the current in the branch with the voltage source is upward and currents in the other two branches are downward, i.e. I_{a} = I_{i} + I_{c}, identify which of the following can be true? Select two answers.
 I_{i} = I_{j}  I_{f}
 I_{e} = I_{h}  I_{i}
 I_{c} = I_{j}  I_{a}
 I_{d} = I_{h}  I_{j}

The measurements reveal that the current through R_{1} is 0.5 A and R_{3} is 0.6 A. Based on your knowledge of Kirchoff’s laws, confirm which of the following statements are true.
 The measured current for R_{1} is correct but for R_{3} is incorrect.
 The measured current for R_{3} is correct but for R_{1} is incorrect.
 Both the measured currents are correct.
 Both the measured currents are incorrect.

The graph shown in the following figure is the energy dissipated at R_{1} as a function of time.
Which of the following shows the graph for energy dissipated at R_{2} as a function of time?

For this question, consider the circuit shown in the following figure.

Assuming that none of the three currents (I_{1}, I_{2}, and I_{3}) are equal to zero, which of the following statements is false?
 I_{3} = I_{1} + I_{2} at point a.
 I_{2} = I_{3}  I_{1} at point e.
 The current through R_{3} is equal to the current through R_{5.}
 The current through R_{1} is equal to the current through R_{5.}

Which of the following statements is true?
 E_{1} + E_{2} + I_{1}R_{1}  I_{2}R_{2} + I_{1}r_{1}  I_{2}r_{2} + I_{1}R_{5} = 0
  E_{1} + E_{2} + I_{1}R_{1}  I_{2}R_{2} + I_{1}r_{1}  I_{2}r_{2}  I_{1}R_{5} = 0
 E_{1}  E_{2}  I_{1}R_{1} + I_{2}R_{2}  I_{1}r_{1} +_{} I_{2}r_{2}  I_{1}R_{5} = 0
 E_{1} + E_{2}  I_{1}R_{1} + I_{2}R_{2}  I_{1}r_{1} + I_{2}r_{2} + I_{1}R_{5} = 0

If I_{1} = 5 A and I_{3} = 2 A, which of the following statements is false?
 The current through R_{1} will flow from a to b and will be equal to 5 A.
 The current through R_{3} will flow from a to j and will be equal to 2 A.
 The current through R_{5} will flow from d to e and will be equal to 5 A.
 None of the above.

If I_{1} = 5 A and I_{3} = 2 A, I_{2} will be equal to
 3 A
 3 A
 7 A
 7 A
In an experiment this circuit is set up. Three ammeters are used to record the currents in the three vertical branches (with R_{1}, R_{2}, and E). The readings of the ammeters in the resistor branches (i.e. currents in R_{1} and R_{2}) are 2 A and 3 A respectively.
 Find the equation obtained by applying Kirchhoff’s loop rule in the loop involving R_{1} and R_{2}.
 What will be the reading of the third ammeter (i.e. the branch with E)? If E were replaced by 3E, how would this reading change?
 If the original circuit is modified by adding another voltage source (as shown in the following circuit), find the readings of the three ammeters.
In this circuit, assume the currents through R_{1}, R_{2} and R_{3} are I_{1}, I_{2} and I_{3} respectively and all are flowing in the clockwise direction.
 Find the equation obtained by applying Kirchhoff’s junction rule at point A.
 Find the equations obtained by applying Kirchhoff’s loop rule in the upper and lower loops.
 Assume R_{1} = R_{2} = 6 Ω, R_{3} = 12 Ω, r_{1} = r_{2} = 0 Ω, E_{1} = 6 V and E_{2} = 4 V. Calculate I_{1}, I_{2} and I_{3}.
 For the situation in which E_{2} is replaced by a closed switch, repeat parts (a) and (b). Using the values for R_{1}, R_{2}, R_{3}, r_{1} and E_{1} from part (c) calculate the currents through the three resistors.
 For the circuit in part (d) calculate the output power of the voltage source and across all the resistors. Examine if energy is conserved in the circuit.
 A student implemented the circuit of part (d) in the lab and measured the current though one of the resistors as 0.19 A. According to the results calculated in part (d) identify the resistor(s). Justify any difference in measured and calculated value.
21.6 DC Circuits Containing Resistors and Capacitors
A battery is connected to a resistor and an uncharged capacitor. The switch for the circuit is closed at t = 0 s.
While the capacitor is being charged, which of the following is true?
 Current through and voltage across the resistor increase.
 Current through and voltage across the resistor decrease.
 Current through and voltage across the resistor first increase and then decrease.
 Current through and voltage across the resistor first decrease and then increase.

When the capacitor is fully charged, which of the following is NOT zero?
 Current in the resistor.
 Voltage across the resistor.
 Current in the capacitor.
 None of the above.
An uncharged capacitor C is connected in series (with a switch) to a resistor R_{1} and a voltage source E. Assume E = 24 V, R_{1} = 1.2 kΩ and C = 1 mF.
 What will be the current through the circuit as the switch is closed? Draw a circuit diagram and show the direction of current after the switch is closed. How long will it take for the capacitor to be 99% charged?
 After full charging, this capacitor is connected in series to another resistor, R_{2} = 1 kΩ. What will be the current in the circuit as soon as it’s connected? Draw a circuit diagram and show the direction of current. How long will it take for the capacitor voltage to reach 3.24 V?