Verified Solution • 2025–26 Session moderate

QPages 165-170: Q4: HC Verma: Concepts of Physics - Volume 2 Capacitors Pages 165-170: Q4 Solution: A parallel-plate capacitor having plate area and separation…

A parallel-plate capacitor having plate area 25 cm225 \text{ cm}^2 and separation 1.00 mm is connected to a battery of 6.0 V. Calculate the charge flown through the battery. How much work has been done by the battery during the process?

Step-by-Step Verified Solution

**Answer:** Q=1.33×10−10Q = 1.33 \times 10^{-10} C, W=8×10−10W = 8 \times 10^{-10} J. **Step-by-Step Explanation:** A=25A = 25 cm_ =2.5×10−3= 2.5 \times 10^{-3} m_, d=1d = 1 mm =10−3= 10^{-3} m, V=6V = 6 V.
C=ϵ0Ad=8.854×10−12×2.5×10−310−3=2.21×10−11 FC = \frac{\epsilon_0 A}{d} = \frac{8.854 \times 10^{-12} \times 2.5 \times 10^{-3}}{10^{-3}} = 2.21 \times 10^{-11} \text{ F}
Q=CV=2.21×10−11×6=1.33×10−10 CQ = CV = 2.21 \times 10^{-11} \times 6 = 1.33 \times 10^{-10} \text{ C}
W=QV=1.33×10−10×6=8×10−10 JW = QV = 1.33 \times 10^{-10} \times 6 = 8 \times 10^{-10} \text{ J}

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