Question

In an oscillating LC circuit, when 86.6% of the total energy is stored in the inductor's magnetic field, (a) what multiple of the maximum charge is on the capacitor and (b) what multiple of the maximum current is in the inductor

Answer 1

We have that for the Question "(a) what multiple of the maximum charge is on the capacitor and (b) what multiple of the maximum current is in the inductor"  

Answer:

• a) maximum charge =  $0.366Q_{max$

• b) maximum current = $0.931I_{max}$

From the question we are told

In an oscillating LC circuit, when 86.6% of the total energy is stored in the inductor's magnetic field

A) When 86.6\% energy is stored in inductor

$\%$of energy stored in electric field = $1 - 0.866 = 13.4\%$

$\frac{V_E}{V} = \frac{\frac{q^2}{2c}}{\frac{Q^2}{2c}} = 0.134\\\\\frac{q}{Q} = \sqrt0.134\\\\\frac{q}{Q} = 0.366\\\\q = 0.366Q_{max$

B)

$\frac{V_B}{V} = \frac{\frac{Li^2}{2}}{\frac{LI^2}{2}} = 0.866\\\\\frac{i}{I} = \sqrt0.866\\\\\frac{i}{I} = 0.931\\\\i = 0.931I_{max$

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