1.)An alternating voltage of v = 1.0 sin 500t + 0.5 sin 1500t is applied across a capacitor which can be represented by a capacitance of 0.5 μF shunted by a resistance of 4,000 Ω. Determine:
(i) the r.m.s. value of the current
(ii) the r.m.s. value of the applied voltage
(iii) the p.f. of the circuit
[Kindly include the circuit diagram in the answer]
2.) An e.m.f. e = 200 sin ωt + 40 sin 3 ωt + 10 sin 5 ωt is impressed on a circuit comprising of a resistance of 10 Ω, a variable inductor and a capacitance of 30 μF, all connected in series. Find the value of the inductance which will give resonance with triple frequency component of the pressure and estimate the effective p.f. of the circuit, ω = 300 radian/second.
3.) A coil having R = 100 Ω and L = 0.1 H is connected in series with a capacitor across a supply, the voltage of which is given by e = 200 sin 314t + 5 sin 3454t. What capacitance would be required to produce resonance with the 11th harmonic. Find:
(a) the equation of the current and,
(b) the r.m.s. value of the current, if this capacitance is in circuit