Answer :
The value of the capacitor in the given circuit is 74.24 μF.
The given parameters;
- Resistance of the resistor, R = 30 ohms
- Initial current = I₀
- Final current, I = 0.26I₀
- Time of discharge, t = 3 ms = 0.003 s
The current on the given plate will decrease exponentially as shown below;
[tex]I = I_0 \times e ^{\frac{-t}{RC} }[/tex]
[tex]0.26I_0 = I_0 \times e^{\frac{-0.003}{30C} }\\\\0.26 = e^{\frac{-0.003}{30C} }\\\\ln(0.26) = \frac{-0.003}{30C} \\\\-1.347 = \frac{-0.003}{30C}\\\\C = \frac{0.003}{1.347 \times 30} \\\\C = 7.424 \times 10^{-5} \ F\\\\C = 74.24 \times 10^{-6} \ F\\\\C = 74.24 \ \mu F[/tex]
Thus, the value of the capacitor in the given circuit is 74.24 μF.
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