Question

As show in the figure, in the steady state, the charge stored in the capacitor is _________ × 10^–6 C.

Fig. 

Answer 1

Correct Answer: 10

In the steady state, the capacitor is fully charged, and no current flows through it. This means the voltage across the capacitor, \( V_c \), is equal to the voltage across the resistor \( R \) because they are in parallel.

The total voltage \( V \) across the entire circuit is 10 V (given by the battery). The current, \( I \), flowing through resistors \( r \) and \( R \) can be determined by the voltage divider rule:

\( V_R = V \cdot \frac{R}{R + r} = 10 \cdot \frac{100}{100 + 10} = 9.09\,\text{V} \)

Now, the voltage across the capacitor is \( V_c = V_R = 9.09 \, \text{V} \).

The charge \( Q \) stored in a capacitor is given by \( Q = C \cdot V_c \), where \( C \) is the capacitance:

\( Q = 1.1 \times 10^{-6} \, \text{F} \cdot 9.09 \, \text{V} = 10 \times 10^{-6}\,\text{C} \)

This value, \( 10 \times 10^{-6}\,\text{C} \), is within the range (10, 10).