Question

At steady state, the charge on the capacitor, as shown in the circuit below, is -----\( \mu C \). 

Hint:

At steady state, a capacitor acts like an open circuit in a DC circuit, and the charge on the capacitor can be calculated using \( Q = C \cdot V \).

Answer 1

Correct Answer: 16

To determine the capacitor charge at steady state, consider the circuit elements and principles. In a DC circuit at steady state, a capacitor functions as an open circuit, preventing current flow and establishing a constant voltage across it.

For a circuit containing resistors and a DC voltage source, follow these steps:

1. Identify the circuit's voltage source (\(V\)).

2. Note the configuration of resistors and capacitors (series/parallel).

3. At steady state, the capacitor charges to the voltage across it. If a single capacitor is present, this voltage equals the source voltage (\(V\)).

4. Calculate the charge (\(Q\)) using the formula: \(Q = C \cdot V\), where \(C\) is capacitance in farads and \(V\) is voltage in volts.

Assuming from the image that:

The voltage across the capacitor (\(V\)) is equivalent to the circuit's supply voltage or the potential difference across it.

The capacitance (\(C\)) is provided or can be determined.

Substituting the values:

Given: capacitance \(C = 1 \mu F\), voltage \(V = 16 V\).

Calculation:

\(Q = 1 \times 10^{-6} \, F \cdot 16 \, V = 16 \times 10^{-6} \, C\)

The charge on the capacitor is \(16 \, \mu C\).

This calculated charge of \(16 \, \mu C\) falls within the expected range of 16,16.