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Question: An LC circuit contains a 20 mH inductor and a 25\(\mu F\)capacitor with an initial charge of 5mC. Th...

An LC circuit contains a 20 mH inductor and a 25μF\mu Fcapacitor with an initial charge of 5mC. The total energy stored in the circuit initially is

A

5 J

B

0.5 J

C

50 J

D

500 J

Answer

0.5 J

Explanation

Solution

: Here, C = 25 μF=25×10−6F,\mu F = 25 \times 10^{- 6}F,

L=20mH=20×10−3HL = 20mH = 20 \times 10^{- 3}H

q0=5mC=5×10−3Cq_{0} = 5mC = 5 \times 10^{- 3}C

∴\therefore Total energy stored in the circuit initially is

U=q022C=(5×10−3)22×25×10−6=25×10−62×25×10−6U = \frac{q_{0}^{2}}{2C} = \frac{(5 \times 10^{- 3})^{2}}{2 \times 25 \times 10^{- 6}} = \frac{25 \times 10^{- 6}}{2 \times 25 \times 10^{- 6}}

=12=0.5J= \frac{1}{2} = 0.5J