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Q7.7  A charged $30\mu F$ capacitor is connected to a $27mH$  inductor. What is the angular frequency of free oscillations of the circuit?

Given Capacitance   Inductance  Now, Angular Frequency  Hence Angular Frequency is

Q7.6  Obtain the resonant frequency $\omega _{r}$ of a series $LCR$ circuit with $L=2.0H$$C=32\mu F$ and  $R=10\Omega$ . What is the Q -value of this circuit?

Given, in a circuit, Inductance,   Capacitance,     Resistance,  Now, Resonance frequency (frequency of maximum current OR minimum impedance OR frequency at which inductive reactance cancels out capacitive reactance ) Hence Resonance frequency is 125 per second. Q-Value:  Hence Q - value of the circuit is 25.

Q7.5  In Exercises 7.3 and 7.4, what is the net power absorbed by each circuit over a complete cycle. Explain your answer.

As we know, Power absorbed  Where  is the phase difference between voltage and current.  for the inductive circuit is -90 degree and  for the capacitive circuit is +90 degree. In both cases (inductive and capacitive), the power absorbed by the circuit is zero because in both cases the phase difference between current and voltage is 90 degree. This can be seen as The elements(Inductor and...

Q7.4   $60\mu F$ capacitor is connected to a $100\: V$$60\; Hz$  ac supply. Determine the rms value of the current in the circuit.

Given, Supply Voltage  Supply Frequency  The capacitance of the connected capacitor    Now, Capacitive Reactance   RMS Value of current Hence the RMS Value of current is 2.49A.

Q7.3  $44\: mH$  inductor is connected to $220\: V$$50\: Hz$  ac supply. Determine the RMS value of the current in the circuit.

Given Supply Voltage  Supply Frequency  The inductance of the inductor connected  Now Inductive Reactance   RMS Value of the current : Hence the RMS Value of current is 15.92A.

Q7.2 (b) The RMS value of current in an ac circuit is $10\: A$ . What is the peak current?

Given, RMS value of current  Since Current is also sinusoidal (because only resistance is present  in the circuit, not the capacitor and inductor) Hence the peak value of current is 14.1A.

Q7.2 (a) The peak voltage of an ac supply is $300 V$. What is the RMS voltage?

Given Peak Value of ac supply:   Now as we know in any sinusoidal function   Since our ac voltage  supply is also sinusoidal Hence RMS value of voltage os 212.13V.

Q7.1 (c) $100\Omega$ resistor is connected to a $220\: V$$50\: Hz$ ac supply.

What is the net power consumed over a full cycle?

Given, Supplied RMS Voltage  Supplied RMS Current The net power consumed over a full cycle: Hence net power consumed is 484W.

Q7.1 (a) $100\Omega$ resistor is connected to a $220\: V$$50\: Hz$ ac supply.

a)what is the RMS value of current?

Given,  RMS voltage in the circuit  Resistance in the circuit  Now, RMS current in the circuit: Hence, the RMS value of current is 2.2A.

3.2 A battery of emf 10 V and internal resistance 3 Ω is connected to a resistor. If the current in the circuit is 0.5 A, what is the resistance of the resistor? What is the terminal voltage of the battery when the circuit is closed?

Given, Emf of the battery, E = 10 V The internal resistance of the battery, r = 3  Current in the circuit, I = 0.5 A Let R be the resistance of the resistor. Therefore, according to Ohm's law: E = IR' = I(R + r)  10 = 0.5(R + 3) R = 20 - 3 = 17  Also, V = IR (Across the resistor) = 0.5 x 17 = 8.5 V Hence, terminal voltage across the resistor = 8.5 V
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