Question

A particular capacitor is initially charged. Then a high-resistance Nichrome wire is connected between the plates of the capacitor, as shown in Figure 19.69. The needle of a compass placed under the wire deflects $\mathbf{20}\mathbf{°}$to the east as soon as the connection is made. After $\mathbf{60}\mathbf{}\mathbf{\text{s}}$the compass needle no longer deflects.

(a)Which of the diagrams in Figure 19.69 best indicates the electron current at three locations in this circuit? (1) $\mathbf{0}\mathbf{.}\mathbf{01}\mathbf{}\mathbf{\text{s}}$after the circuit is connected, (2) $\mathbf{15}\mathbf{}\mathbf{\text{s}}$ after the circuit is connected, (3) $\mathbf{120}\mathbf{}\mathbf{\text{s}}$ after the circuit is connected.

(b)Which of the diagrams in Figure 19.70 best indicates the net electric field inside the wire at three locations in this circuit? (1) $\mathbf{0}\mathbf{.}\mathbf{01}\mathbf{}\mathbf{\text{s}}$ after the circuit is connected, (2) $\mathbf{15}\mathbf{}\mathbf{\text{s}}$after the circuit is connected, (3) $\mathbf{120}\mathbf{}\mathbf{\text{s}}$ after the circuit is connected.

Short answer

(a) (1) Figure (C) best depicts the current in the circuit after$0.01\text{s}$.

(2) Figure (B) best depicts the current in the circuit after$15\text{s}$.

(3) Figure (A) best depicts the current in the circuit after $120\text{s}$.

Step-by-step solution

Given data

A fully charged capacitor is connected to a Nichrome wire. The magnetic deflection under the wire stops after $60\text{s}$.

Discharging of a capacitor

When a fully charged capacitor is connected in a circuit, electron flows from the negative to the positive plate, thus reducing charge in both plates.

(a) Determination of the current in the circuit at different times

As charges flow from the negative plate to the positive plate through the circuit, the net charge in the plates reduces. With decrease in charge of the plates, the fringe field in the circuit decreases thus decreasing the current. This continues till the capacitor is completely discharged and the current in the circuit is zero. Evidently this happens at when there is no further deflection in the magnetic needle. Thus at the discharging has begun and the current is maximum. This is best depicted by figure (C). After the discharging has continued for a while and the current has reduced. This is best depicted by figure (B). After the capacitor is completely discharged and the current is zero. This is best depicted by figure (A).