Alternating Current -06-SUBJECTIVE UNSOLVED LEVEL - II

SUBJECTIVE UNSOLVED LEVEL - II (BRUSH UP YOUR CONCEPTS) 1. A capacitor of capacitance 10 F is connected to an oscillator giving an output voltage   (10 V) sin t . Find the peak currents in the circuit for   10rads1,100rads1, 500rads1,1000rads1 . 2. In a series LCR circuit with an AC source, R = 300  , C = 20 F , L = 1.0 henry, connected to variable voltage 50 V and f = 50/  Hz. Find (a) The rms current in the circuit and (b) The rms potential differences across the capacitor, the resistor and the inductor. Note that the sum of the rms potential differences across the three elements is greater than the rms voltage of the source. 3. An inductance of 2.0 H, a capacitance of 18 F and a resistance of 10 k  are connected to an AC source of 20 V with adjustable frequency. (a) What frequency should be chosen to maximize the current in the circuit ? (b) What is the value of this maximum current ? 4. A transformer has 50 turns in the primary and 100 in the secondary. If the primary is connected to a 220 V DC supply, what will be the voltage across the secondary ? 5. In figure, R = 15.0  , C = 4.72 F , and L = 25.3 mH. The gen- erator provides a sinusoidal voltage of 75.0 V (rms) and frequency f = 550 Hz. (a) Calculate the rms current amplitude (b) Find the rms voltages Vab , Vbc , Vcd , Vad (c) What average power is dissipated by each of the three circuit elements ? 6. An inductor of reactance 10  and a resistance of 10  are connected in series and the combina- tion is connected to a 220-V, 50-Hz a.c. supply. Calculate the current through the circuit. Give the expression for the instantaneous current. 7. The current in a coil of inductance L = 2.0 H is increasing according to the law i = 2 sin t2. Find the amount of energy spent during the period when the current changes from 0 to 2 A. 8. A coil of inductance 0.525 henry is connected to a direct current source of 120 volt. A current of 0.5 ampere flows through the coil. If the coil be connected to an A.C. source of frequency 60 cycle/ second and 120 volt, then what will be the current in the coil ? 9. A circuit contains a resistance of 4 ohm and inductance of 0.68 henry and an alternating effective emf of 500 volt at a frequency of 120 cycles per second applied it. Find the value of effective current in the circuit and power factor. 10. The operating coil of a relay of inductance 8 mH and a resistance of 30 ohm is connected across a 5 V 800 cycle A.C. supply. Find the current through the coil and the phase angle of the current relative to applied voltage. How could this phase angle be reduced to zero without altering the value of the current passing through the coil when the relay is operated from the same A.C. supply ? SUBJECTIVE UNSOLVED LEVEL - III (CHECK YOUR SKILLS) 1. The current in a discharging LR circuit is given by i  i et/  circuit. Calculate the rms current for the period t = 0 to t =  . where  is it the time constant of the 2. An inductor-coil, a capacitor and an AC source of rms voltage 24 V are connected in series. When the frequency of the source is varied, a maximum rms current of 6.0 A is observed. If this inductor coil is connected to a battery of emf 12 V and internal resistance 4.0  , what will be the current ? 3. Figure shows a typical circuit for low-pass filter. An AC input Vi  10mV is applied at the left end and the output Vo V0 is received at the right end. Find the output voltages for f = 10 kHz, 100 kHz, 1.0 MHz and 10.0 MHz. Note that as the frequency is increased the output decreases and hence the name low-pass filter. 4. Show that when a coil of inductance L and resistance R is attached to two terminals at which an emf v  V sin t is maintained, the everage rate of consumption of energy is 1 V2 R / R 2  2 L2  0 2 0 5. A high-impedance AC voltmeter is connected in turn across the inductor, the capacitor, and the resistor in a series circuit having an AC source of 100 V (rms) and gives the same reading in volts in each case. What is this reading ? 6. A certain RLC combination, R1, L1, C1 , has a resonant frequency that is the same as that of a different combination, R2 , L2 , C2 . You now connect the two combinations in series. Show that this new circuit has the same resonant frequency as the separate individual circuits. 7. A circuit consists of a non inductive resistor of 50  , a coil of inductance 0.3 H and resistance 2 , and a capacitor of 40F in series and is supplied with 200 volts rms at 50 cycles/sec. Find the current lag or lead and the power in the circuit. 8. A circuit has a coil of resistance 60 ohm and inductance 3 henry. It is connected in series with a capacitor of 4 F and A.C. supply voltage of 200 V and 50 cycle/sec. Calculate (i) the impedance of the coil (ii) the p.d. across inductor coil and capacitor. 9. Find the current amplitude & phase difference and plot the current as a function of time from the given figure. f = 50 Hz. L = 35 mH R = 11  V = v0 sin t Vrms = 220V 10. A current of 4A flows in a coil when connected to a 12 V d.c. source. If the same coil is connected to 12 V, 50 rad/s.a.c. source a current of 2.4 A flows in the circuit. Determine the inductance of the coil. Also find the power developed in the circuit if 2500 F coil. capacitor is connected in series with the

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