A charged capacitor with C = 780 μF is connected in parallel to an inductor that has L = 0.290 H and negligible resistance. At an instant when the current in the inductor is i = 2.40 A , the current is increasing at a rate of di/dt=89.0A/s.what is the maximum voltage across the capacitor?

Answer :

Answer:52.98 V

Explanation:

Given

[tex]C=780 \mu F\approx 780\times 10^{-6}F[/tex]

[tex]L=0.290 H[/tex]

Current [tex]i=2.4 A[/tex]

[tex]\frac{\mathrm{d} i}{\mathrm{d} t}=89 A/s[/tex]

Now voltage across inductor[tex]=L\frac{\mathrm{d} i}{\mathrm{d} t}[/tex]

[tex]v=0.29\times 89=25.81 V[/tex]

same voltage is around the capacitor as they are in a loop

Total Energy[tex]=\frac{cV^2}{2}+\frac{Li^2}{2}[/tex]

[tex]E=\frac{780\times 10^{-6}\times 25.81^2}{2}+\frac{0.29\times 2.4^2}{2}[/tex]

[tex]E=0.2598+0.8352=1.095 J[/tex]

For maximum Voltage

[tex]\frac{cV_{max}^2}{2}=E[/tex]   (as Energy is constant)

[tex]\frac{780\times 10^{-6}\times V_{max}^2}{2}=1.095[/tex]

[tex]V_{max}^2=2.807\times 10^3[/tex]

[tex]V_{max}=52.98 V[/tex]

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