6. Th e graph shows the voltage across and the current through a single circuit

Question

6. Th e graph shows the voltage across and the current through a single circuit element connected to an ac generator. The peak voltage and current are, respectively, V.-40 V and 1,-5.0A Current Voltage 0.50 0.75 0 0.25 1.00 125 t (ms) r inductance of the (a) Determine the frequency of the generator. (b) What is the resistance, capacitance, o element in the circuit? (You have to identify the element as a resist of these three elements.) or, capacitor, or inductor. It is only one 7. The angular frequency of an LC circuit at which the capacitive reactance is 25 times larger than the inductive reactance is 1000 rad/s. What is the resonant angular frequency of the circuit?

Explanation / Answer

6. We know that

Frequency = 1/t = 1/1.25*10-3

Thus f = 800 Hz.

And we also know that, AccpeAcco to Ohms law,

V= IR ----- equation 1

Substituting v=40 V, I = 5A in Equation 1

Thus, Resistance R = 8 ohms,

For capacitance, we know that

C = 1/(2*3.14*f*R) = C = 24.88 * 10-6 F,

Thus Inductance,

We know that f=1/(2*3.14*sqft(LC))

From this, Sqft(LC) = 1/ (2*3.14*800)

Thus L = 101.44 * 1010 Henry

7. We know that Angular frequency = 1000 rad/s

C = 25L,

We also know that resonant angular frequency is

f = 1/ (2*3.14* sqft(LC)) = angular frequency / 2*3.14

Thus Resonant Angular Frequency f = 5000 L

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