Capacitors: Real-World Scenarios (5)

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Tags Capacitors

Question

A camera flash uses a 10001000 μF capacitor charged to 300300 V. The flash discharges the capacitor through the xenon tube in 11 ms. Find (a) the energy stored, (b) the average power delivered to the flash tube, and (c) the charge stored. JEE Main 2024 style real-world numerical.

Solution — Step by Step

Energy stored in a capacitor:

U=12CV2=12×1000×10−6×3002U = \frac{1}{2}CV^2 = \frac{1}{2} \times 1000 \times 10^{-6} \times 300^2

U=12×10−3×90000=45 JU = \frac{1}{2} \times 10^{-3} \times 90000 = 45 \text{ J}

Q=CV=1000×10−6×300=0.3 CQ = CV = 1000 \times 10^{-6} \times 300 = 0.3 \text{ C}

That’s a substantial charge — which is why charged camera capacitors can deliver dangerous shocks even when the camera is unplugged.

Pavg=UΔt=451×10−3=45000 W=45 kWP_{\text{avg}} = \frac{U}{\Delta t} = \frac{45}{1 \times 10^{-3}} = 45000 \text{ W} = 45 \text{ kW}

U=45U = 45 J, Q=0.3Q = 0.3 C, Pavg=45P_{\text{avg}} = 45 kW.

Why This Works

A capacitor stores energy in the electric field between its plates, given by U=12CV2U = \frac{1}{2}CV^2. The factor of 12\frac{1}{2} comes from integrating V dQV\,dQ as the capacitor charges from 00 to QQ — half the work goes into the field, half (in a resistive charging circuit) is dissipated as heat.

The 45 kW peak power illustrates why capacitors are used for flash photography, defibrillators, and railgun research: they can deliver enormous instantaneous power because they release stored energy in microseconds. A 45 W bulb runs continuously at 45 W; the camera flash matches a small power station for a millisecond.

Alternative Method

Use the alternative formulas U=Q22CU = \dfrac{Q^2}{2C} or U=12QVU = \dfrac{1}{2}QV. Computing 12QV=12×0.3×300=45\dfrac{1}{2}QV = \dfrac{1}{2} \times 0.3 \times 300 = 45 J cross-checks our answer.

Students forget the factor of 12\frac{1}{2} and write U=CV2=90U = CV^2 = 90 J. Always remember: capacitor energy has the half, just like spring energy 12kx2\frac{1}{2}kx^2 and kinetic energy 12mv2\frac{1}{2}mv^2.

For real safety: a capacitor at 300 V with 0.3 C of charge can deliver a lethal shock. Camera and microwave technicians always discharge capacitors with a high-resistance probe before servicing.

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