HSSC-II (12th Class) Physics Unit-15: Alternating Current: Numerical Problems List (New Book/KPK Text Board, Peshawar) With Verified Answers

1: The peak voltage of an ac supply is 300 V. What is the rms voltage? Ans (212.1V) 

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2: The rms value of current in an ac circuit is 10 A. What is the peak current? Ans (14.1 A) 

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3: The a.c. voltage across a 0.5 µF capacitor is 16 sin (2 ｘ 10³ t) V. Find (a) the capacitive reactance (b) the peak value of current through the capacitor. Ans (1000Ω, 16mA) 

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4: The voltage across a 0.01 µF capacitor is 240 sin (1.25 ｘ 10⁴ t - 30°) V. Write the mathematical expression for the current through it. 

Ans (I = 0.03 sin(1.25 ｘ 10⁴ t + 60°) A)

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5: An inductor with an inductance of 100 µH passes a current of 10 mA when its terminal voltage is 6.3 V. Calculate the frequency of A.C supply. Ans (10⁶ Hz) 

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6: (a) Calculate the inductive reactance of a 3.00 mH inductor, when 60.0 Hz and 10.0 kHz AC voltages are applied. (b) What is the rms current at each frequency if the applied rms voltage is 120 V? Ans ((a) 1.13 Ω, 188 Ω (b) 106 A, 0.637 A) 

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7: For the same RLC series circuit having a 40.0 Ω resistor, a 3.00 mH inductor, and a 5.00 µF capacitor: (a) Find the resonant frequency. (b) Calculate Iᵣₘₛ at resonance if Vᵣₘₛ is 120 V. Ans ( (a) 1.30 kHz, (b) 3.00 A)  

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8: A resistor of resistance 30 Ω is connected in series with a capacitor of capacitance 79.5 µF across a power supply of 50Hz and 100V. Find (a) impedance (b) current (c) phase angle and (c) equation for the instantaneous value of current. Ans (a. 50 Ω, b. 2A, c. 53° lead, d. 2.828 sin (314t + 53°) 

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9: A coil having a resistance of 7 Ω and an inductance of 31.8 mH is connected to 230V, 50Hz supply. Calculate (a) the circuit current (b) phase angle (c) power factor. (d) power consumed. Ans (18.85, 55° lag, .573° lag, 2484.24 w) 

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10: A capacitor which has a resistance of 10 Ω and a capacitance value of 100 µF is connected to a supply voltage given as V₍ₜ₎ = 100 sin (314t). Calculate the capacitive reactance, circuit impedance and peak current flowing into the capacitor. Ans (31.85 Ω, 33.4 Ω and 3A )

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