Question

Question: in circuit 1 (Figure 19.72), an uncharged capacitor is connected in series with two batteries and one light bulb. Circuit 2 (Figure 19.72) contains two light bulbs identical to the bulb in the circuit; in all other respects, it is identical to circuit 1. In circuit 1, the light bulb stays lit for 25 s. The following questions refer to these circuits. You should draw diagrams representing the fields and charges in each circuit at the times mentioned, in order to answer the questions.

(a)One microsecond after connecting both circuits, which of the following are true? Chose all that apply: (1) the net electric field at location B in circuit 1 is larger than the net electric field at location B in circuit 2. (2) At location A in 1, electrons flow to the left. (3) At location A in circuit 1, the electric fields due to charges on the surface of the wires and batteries points to the right. (4) in circuit 1 the potential difference across the capacitor plates is equal to the emf of the batteries. (5) The current in circuit 1 is larger than the current in circuit 2.

(b)Two seconds after connecting both circuits, which of the following are true? Choose all that apply: (1) there is more charge on the plates of capacitor 1 than there is on the plates of capacitor 2. (2) there is negative charge on the right plate of the capacitor in circuit 1. (3) At location B in circuit 2 the net electric field points to the right. (4) At location B in circuit 2 the fringe field of the capacitor points to the right. (5) At location A in circuit 1 the fringe field of the capacitor points to the left.

(c)Which of the graphs in Figure 19.73 represents the amount of charge on the positive plate of the capacitor in circuit 1 as a function of time?

(d)Which of the graphs in Figure 19.73 represents the current in circuit 1 as a function of time?

Short answer

(a)

1. The electric field at location A is greater than the location at B is true.
2. The electron current moving left from point A in circuit 1 is true.
3. The electric field direction of the battery and wire towards the right side of A is true.
4. If the potential difference across the capacitor and batteries are equal current will not flow and charging of the battery is not taken place hence the statement is false.
5. Current in the circuit 1 is greater than the current in circuit 2 is true since the higher is the resistance value in an identical circuit lower is current.

(b)

1. Two seconds after the charge on capacitor 1 is more than the charge on capacitor 2 is true.
2. The negative charge on the right side plate of capacitor 1 is true.
3. At point B electric field direction towards the right side is true since the electron current moves towards the left side from point B.
4. At location B of circuit 2 fringe field of the capacitor point towards the left side and hence the statement is false.
5. At location A of circuit 1 fringe field of the capacitor point towards the left side and hence the statement is true.

(c) The graph (C) in Figure 19.73 represents the amount of charge on the positive plate of the capacitor in circuit 1 as a function of time.

(d) Graph (A) in Figure 19.73 represents the current flowing through the capacitor in circuit 1.

Step-by-step solution

A concept:

The capacitor is fully charged when the supply voltage is the same as that across the capacitor terminals. This is called capacitor charging and the charging phase is over when the electric circuit stops flowing current. After disconnecting the power source from the capacitor, the discharge phase begins.

(a) Which of the following are true?

(1) Current flowing through circuit 1 is more than the current flow through circuit 2 and hence electric field at location A is greater than the electric field at location B. Therefore electric field at location A is greater than the location at B is true.

(2)During the charging of the capacitor electron current moves away from the positive plate. And hence electron current moves left from point A in circuit 1 is true.

(3) In the charging of the capacitor, the positive charge of the plate increases due to the movement of the negative charge away from a positive plate which is the electric field direction of wires and batteries should be the opposite of the electron current that is the right side of A for circuit 1.

And hence electric field direction of the battery and wire towards the right side of A is true.

(4) If the potential difference across the capacitor and batteries are equal current will not flow and charging of the battery is not taken place. Hence the statement is false.

(5) Current in the circuit 1 is greater than the current in circuit 2 is true since the higher is the resistance value in an identical circuit lower is current.

(b) Which of the following are true?

(1) Two seconds after the charge on capacitor 1 is more than the charge on capacitor 2 is true, the higher is current flow the circuit higher is charge accumulation.

(2) The negative charge on the right side plate of capacitor 1 is true.

(3) At point B electric field direction towards the right side is true since the electron current moves towards the left side from point B.

(4) At location B of circuit 2 fringe field of the capacitor point towards the left side and hence the statement is false.

(5) At location A of circuit 1 fringe field of the capacitor point towards the left side and hence the statement is true.

(c) About the given graph:

Graph $\left(C\right)$represents the charging of the positive plate of the capacitor in circuit 1 since the initial charge on the capacitor is zero gradually charge on the capacitor increase and finally reaches the maximum value.

Hence, graph $\left(C\right)$in Figure 19.73 represents the amount of charge on the positive plate of the capacitor in circuit 1 as a function of time.

(d) About the given graph:

Graph $\left(A\right)$represents the current flowing the capacitor in circuit 1 since initially current flow through capacitor is maximum gradually current on capacitor decreases and finally reaches the zero value.

Hence, a graph $\left(A\right)$in Figure 19.73 represents the current flowing through the capacitor in circuit 1.