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=20sin(100πt+π3) A. The voltage across the inductance L of 0.1 H at t=0 will be
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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