An L C circuit consists of a 20.0- mH inductor and a 0.500-μ F capacitor. If the maximum instantaneous current is 0.100 A, the greatest potential difference across the capacitor (in V) is

Question

An L C circuit consists of a 20.0- mH inductor and a 0.500-μ F capacitor. If the maximum instantaneous current is 0.100 A, the greatest potential difference across the capacitor (in V) is (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

At different times, the maximum energy stored in the capacitor is equal to the maximum energy stored in the inductor.

[\frac{1}{2} C (Δ V)^{2}]_{m a x} = \frac{1}{2} L I_{i}^{2}

So (Δ V_{c})_{m a x} = \frac{L}{C} I_{i}

= \frac{20.0 \times 1 0 ^{- 3}}{0.500 \times 1 0 ^{- 6}} (0.100) = 20.0 V

Q. An LC circuit consists of a 20.0−mH inductor and a 0.500−μF capacitor. If the maximum instantaneous current is 0.100A, the greatest potential difference across the capacitor (in V) is

At different times, the maximum energy stored in the capacitor is equal to the maximum energy stored in the inductor. [21​C(ΔV)2]max​=21​LIi2​ So (ΔVc​)max​=CL​​Ii​ =0.500×10−620.0×10−3​(0.100)​=20.0V

Q. An $L C$ circuit consists of a $20.0 - m H$ inductor and a $0.500 - μ F$ capacitor. If the maximum instantaneous current is $0.100 A$ , the greatest potential difference across the capacitor (in $V$ ) is