Numerical Problems Chapter 15 Alternating Current l 2nd Year Physics Federal Board (KPK Syllabus)

Give extended response to the following questions
Define mean, peak and rms value of sinusoidal current and sinusoidal voltage. Obtain mathematical expression for the rms value of current.
A sinusoidal alternating voltage of angular frequency ω is connected across a resistor R. Find mathematical expression for instantaneous voltage, instantaneous current and the average power dissipated per cycle of the applied voltage.
A sinusoidal alternating voltage of angular frequency ω is connected across a capacitor C. Find mathematical expression for instantaneous voltage, instantaneous current and the average power dissipated per cycle of the applied voltage.
Explain the term impedance of an AC circuit. Find expression for the RLC series circuit.
Describe that maximum power is transferred when the impedance of source and load match to each other.
In an RL series circuit will the current lag or lead the applied alternating voltage? Explain the answer with a phasor diagram.
In an RC series circuit will the current lag or lead the applied alternating voltage? Explain the answer with a phasor diagram.
Describe the statement of four Maxwell’s equations. Using Maxwell’s theory show that
E=1/2 (∆∅)/∆t=A/2πr ∆B/∆t & I=(ε_o ∆(∅))/∆t
Describe the principle of metal detectors with suitable diagram.
Sketch a graph of e.m.f. induced in an inductive coil against rate of change of current. What is the significance of the gradient?
Current and voltage provided by an AC generator are sometimes negative and sometimes positive. Why for, an AC generator connected to a resistor, power can never be negative?
What determines the gradient of a graph of inductive reactance against frequency?
How does doubling the frequency affect the reactance of (a) an inductor (b) a capacitor?
If the peak value of a sine wave is 1000 volts, what is the effective value?
Show that reactance is measured in ohms for both inductors and capacitors.
What is the principle of ECG?
The peak voltage of an ac supply is 300V. What is the rms voltage?
The rms value of current in an ac circuit is 10A. What is the peak current?
The a.c. voltage across a 0.5μF capacitor is 16sin(2×〖10〗^3 t)V. Find (a) the capacitive reactance (b) the peak value of current through the capacitor.
The voltage across a 0.01μF capacitor is 240sin(1.25×〖10〗^4 t-30°)V. Write the mathematical expression for the current through it.
An inductor with an inductance of 100μH passes a current of 10mA when its terminal voltage is 6.3V. Calculate the frequency of A.C supply.
(a) Calculate the inductance of a 3.00mH inductor, when 60.0Hz and 10.0kHz AC voltages are applied. (b) What is the rms current at each frequency if the applied rms voltage is 120V?
For the same RLC series circuit having a 40.0Ω resistor, a 3.00mH inductor, and a 5.00µF capacitor: (a) Find the resonant frequency. (b) Calculate I_rms at resonance if V_rms is 120V.
A resistor of resistance 30Ω is connected in series with a capacitor of capacitance 79.5µF across a power supply of 50Hz and 100V. Find (a) impedance (b) current (c) phase angle and (d) equation for the instantaneous value of current.
Coil having a resistance of 7Ω and an inductance of 31.8mH is connected to 230V, 50Hz supply. Calculate (a) the circuit current (b) phase angle (c) power factor (d) power consumed.
A capacitor which has a resistance of 10Ω and a capacitance value of 100µF is connected to a supply voltage given as V_((t))=100sin(314t). Calculate the capacitive reactance, circuit impedance and peak current flowing into the capacitor.