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A 50μf capacitor in a defibrillator is charged to 3000V. The energy stored in the capacitor is sent through the victim during a pulse of duration 2 ms
Question

A 50μf capacitor in a defibrillator is charged to 3000V. The energy stored in the capacitor is sent through the victim during a pulse of duration 2 ms; the power of the pulse is close to:

A.

50 kW

B.

75 kW

C.

112.5 kW

D.

200 kW

Correct option is C

Given:Capacitance, C=50 μF=50×106 FVoltage, V=3000 VTime, t=2 ms=2×103 sEnergy stored in a capacitor:E=12CV2Power:P=Et EnergyE=12×50×106×(3000)2E=25×106×9×106=225 J PowerP=2252×103=112500 W=112.5 kW\textbf{Given:} \\\bullet \text{Capacitance, } C = 50\, \mu F = 50 \times 10^{-6}\, F \\\bullet \text{Voltage, } V = 3000\, V \\\bullet \text{Time, } t = 2\, ms = 2 \times 10^{-3}\, s\\[10pt] \text{Energy stored in a capacitor:} \quad E = \frac{1}{2} C V^2 \\ \text{Power:} \quad P = \frac{E}{t}\\[10pt]\textbf{ Energy} \\E = \frac{1}{2} \times 50 \times 10^{-6} \times (3000)^2 \\E = 25 \times 10^{-6} \times 9 \times 10^6 = 225\, J\\[10pt]\textbf{ Power} \\P = \frac{225}{2 \times 10^{-3}} = 112500\, W = 112.5\, \text{kW}​​

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