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Question
Find the charge on the capacitor shown in the figure.
Solution
In steady state, the capacitor is fully charged and then, it offers infinite resistance to the direct current flow. So, no current can flow through the capacitor in steady state.
The effective resistance of the circuit,
Reff = 10 + 20 = 30 Ω
The current i through the circuit,
\[i = \frac{2}{30} = \frac{1}{15} A\]
Voltage drop across the 10 Ω resistor,
V = i × r
\[= \frac{1}{15} \times 10\]
\[ = \frac{10}{15} = \frac{2}{3} V\]
Since the potential drops across the capacitor and the 10 Ω resistor are the same,
the charge stored on the capacitor,
Q = CV
\[= 6 \times {10}^{- 6} \times \frac{2}{3}\]
\[ = 4 \times {10}^{- 6} C = 4 mC\]
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