An RLC circuit has a resistance of 200 $\Omega$ and an inductance of 15 mH.Its oscillation frequency is 7000 Hz.At time t = 0 the current is 25 mA and there is no charge on the capacitor.After five complete cycles the current is: A)0 A B)1.8 * 10^-6 A C)2.1 *10^-4 A D)2.3 * 10^-3 A E)2.5 * 10^-2 A

Question

Quizplus · Accepted Answer

The formula for the current in an RLC circuit at any time t is given by:

I(t) = Imax*e^(-Rt/L)*cos(wt - phi)

where Imax is the maximum current, R is the resistance, L is the inductance, w is the angular frequency (2*pi*f), and phi is the phase angle.

In this circuit, R = 200 ohms, L = 15 mH, and f = 7000 Hz. Therefore, w = 2*pi*f = 44070 rad/s.

At time t = 0, the current is 25 mA and there is no charge on the capacitor. This means that the capacitor is initially a short circuit (acting as a wire) and the circuit is purely inductive. Therefore, the initial phase angle phi is 90 degrees.

After five complete cycles, the phase angle has shifted by 5*360 degrees = 1800 degrees. Therefore, the phase angle is now 90 + 1800 = 1890 degrees.

Using these values, we can calculate the current using the formula:

I(t) = Imax*e^(-Rt/L)*cos(wt - phi)

At time t = 5/f = 0.000714 s (which is the time for 5 cycles), we have:

I(0.000714) = 0.025*exp(-200*0.000714/0.015)*cos(44070*0.000714 - 1890)

Solving for I(0.000714), we get:

I(0.000714) = 2.13*10^-4 A

Therefore, the answer is (C) 2.1*10^-4 A.

An RLC Circuit Has a Resistance of 200 Ω\OmegaΩ And an Inductance of 15 MH

An RLC Circuit Has a Resistance of 200 $\Omega$ And an Inductance of 15 MH