In the circuit shown, the charge on the capacitor versus time is given by the ex

Question

In the circuit shown, the charge on the capacitor versus time is given by the expression Q = 25 r^2 [r is in seconds, Q is in Coulombs] The is a time dependent voltage source. The resistance R = 6 Ohms. The inductance L = 3 Henries. The capacitance C = 5 Farads. (a) Calculate the current I versus time t. (b) Calculate the potential difference V_c-V_phi versus time t. (c) Calculate the potential differential V_ - V_ versus time r. (d) Calculate the potential difference V_ -V_ versus time t. (e) Calculate the versus time t.

Explanation / Answer

Given that

Charge Q=25t^2

Now we find the current vs time

Current I=d/dt(25t^2)=50t

Now we find potential difference Vc-Vd vs time

Vc-Vd=50t(2**L/t)

=50*2**3

=300

Now we find the potential difference Va-Vbversus time

Va-Vb=50t*6=300t

Now we find the potential difference Vb-Vc versus time

Vb-Vc=50t(t/2**3)

=25t^2/3

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