Question

When a particular capacitor, which is initially uncharged, is connected to a battery and a small light bulb, the light bulb is initially bright but gradually gets dimmer, and after $\mathbf{45}\mathbf{}\mathbf{\text{s}}$ it goes out. The diagrams in Figure 19.71 show the electric field in the circuit and the surface charge distribution on the wires at three different times ( $\mathbf{0}\mathbf{.}\mathbf{01}\mathbf{}\mathbf{\text{s}}$, $\mathbf{8}\mathbf{}\mathbf{\text{s}}$, and $\mathbf{240}\mathbf{}\mathbf{\text{s}}$) after the connection to the bulb is made. Which of the diagrams best represents the state of the circuit at each time specified?

(a)$\mathbf{0}\mathbf{.}\mathbf{01}\mathbf{}\mathbf{\text{s}}$after the connection is made,

(b)$\mathbf{8}\mathbf{}\mathbf{\text{s}}$after the connection is made,

(c)$\mathbf{240}\mathbf{}\mathbf{\text{s}}$after the connection is made.

Short answer

(a) Figure (C) best depicts the field and charge distribution in the circuit $0.01\text{s}$ after the connection is made.

Step-by-step solution

Given data

A capacitor and a bulb is connected in series with two batteries. The bulb gradually gets dimmer, and after $45\text{s}$ it goes out.

Flow of charges

As soon as it is switched on, positive charges flow away from the positive terminal of the battery and negative charges flow away from the negative terminal of the battery. This flow is due to the field created by the battery.

(a) Determination of the depiction of the circuit   after the connection is made

As soon as the connection is made, positive charges start flowing out of the positive terminal and negative charges start flowing out of the negative terminal. This constitutes a current and the current lights the bulb. The figure that best depicts the situation in (C).