The current in an LCR circuit is given by I=20sin(100πt+π3) A. The voltage across the inductance L of 0.1 H at t=0 will be

Question

The current in an LCR circuit is given by

$I = 20 \sin(100\pi t + \frac{\pi}{3}) \, \text{A}$

The voltage across the inductance L of 0.1 H at t=0 will be.

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Solution

The voltage across an inductor is given by the formula V = L * di/dt, where L is the inductance and di/dt is the rate of change of current with respect to time.

Given the current I = 20sin(100πt + π/3) A, we can differentiate this with respect to time to find di/dt.

The derivative of sin(x) is cos(x), and the derivative of the inside function 100πt + π/3 is 100π. So, using the chain rule, we get:

di/dt = 20 * 100π * cos(100πt + π/3)

At t = 0, this becomes:

di/dt = 2000π * cos(π/3) = 2000π * 1/2 = 1000π A/s

Now we can substitute this into the voltage formula:

V = L * di/dt = 0.1 H * 1000π A/s = 100π V

So, the voltage across the inductance L of 0.1 H at t = 0 is 100π volts.

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The current in an LCR circuit is given by I=20sin(100πt+π3) A. The voltage across the inductance L of 0.1 H at t=0 will be

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