Aseries circuit has a capacitor of 0.25 × 10⁻⁶ f, a resistor of 5 × 10³ ω, and an inductor of 1h. the initial charge on the capacitor is zero. if a 12 v battery is connected to the circuit and the circuit is closed at t = 0, determine the charge on the capacitor at t = 0.001 s, at t = 0.01 s, and at any time t. also determine the limiting charge as t → [infinity].

at t = 0.001 we have

at t = 0.01

at t = infinity

Explanation:

As we know that they are in series so the voltage across all three will be sum of all individual voltages

so it is given as

now we will have

now we have

So we will have

at t = 0 we have

q = 0

also we know that

at t = 0 i = 0

so we have

at t = 0.001 we have

at t = 0.01

at t = infinity

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explanation: