A 100 ? resistor is connected to a 220 V, 50 Hz ac supply. (I) What is the rms value of current in thecircuit? (II) What is the net power consumed over a full cycle?

(I) The peak voltage of an ac supply is 300 V. What is the rmsvoltage? (II) The rms value of current in an ac circuit is 10 A. What is the peakcurrent?

A 44 mH inductor is connected to 220 V, 50 Hz ac supply. Determine the rms value of the current in the circuit.

A 60 µF capacitor is connected to a 110 V, 60 Hz ac supply. Determine the rms value of the current in the circuit.

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

Obtain the resonant frequency ?r of a series LCR circuit with L = 2.0 H, C = 32 µF and R= 10 ?. What is the Q-value of this circuit?

A charged 30 µF capacitor is connected to a 27 mH inductor. What is the angular frequency of free oscillations of the circuit?

Suppose the initial charge on the capacitor in Exercise 7.7 is 6 mC. What is the total energy stored in the circuit initially? What is the total energy at later time?

A series LCR circuit with R = 20 ?, L = 1.5 H and C = 35 µF is connected to a variable- frequency 200 V ac supply. When the frequency of the supply equals the natural frequency of the circuit, what is the average power transferred to the circuit in one complete cycle?

A radio can tune over the frequency range of a portion of MW broadcast band: (800 kHz to 1200 kHz). If its LC circuit has an effective inductance of 200 µH, what must be the range of its variable capacitor? [Hint: For tuning, the natural frequency i.e., the frequency of free oscillations of the LCcircuit should be equal to the frequency of the radiowave.]

Figure 7.21 shows a series LCR circuit connected to a variable frequency 230 V source. L = 5.0 H, C = 80µF, R = 40 ? (I) Determine the source frequency which drives the circuit inresonance. (II) Obtaintheimpedanceofthecircuitandtheamplitudeofcurrentattheresonating frequency. (III) Determine the rms potential drops across the three elements of the circuit. Show that the potential drop across the LC combination is zero at the resonating frequency.

An LC circuit contains a 20 mH inductor and a 50 µF capacitor with an initial charge of 10 mC. The resistance of the circuit is negligible. Let the instant the circuit is closed be t = 0. (I) What is the total energy stored initially? Is it conserved during LCoscillations? (II) What is the natural frequency of thecircuit? (III) At what time is the energystored (IV) completelyelectrical(i.e.,storedinthecapacitor)?(ii)completelymagnetic(i.e., stored in theinductor)? (V) Atwhattimesisthetotalenergysharedequallybetweentheinductorandthe capacitor? (VI) Ifaresistorisinsertedinthecircuit,howmuchenergyiseventuallydissipatedas heat?

A coil of inductance 0.50 H and resistance 100 ? is connected to a 240 V, 50 Hz ac supply. (I) What is the maximum current in thecoil? (II) What is the time lag between the voltage maximum and the current maximum?

Obtain the answers (a) to (b) in Exercise 7.13 if the circuit is connected to a high frequency supply (240 V, 10 kHz). Hence, explain the statement that at very high frequency, an inductor in a circuit nearly amounts to an open circuit. How does an inductor behave in a dc circuit after the steady state?

A 100 µF capacitor in series with a 40 ? resistance is connected to a 110 V, 60 Hz supply. (I) What is the maximum current in thecircuit? (II) What is the time lag between the current maximum and the voltage maximum?

Obtain the answers to (a) and (b) in Exercise 7.15 if the circuit is connected to a 110 V, 12 kHz supply? Hence, explain the statement that a capacitor is a conductor at very high frequencies. Compare this behaviour with that of a capacitor in a dc circuit after the steady state.

Keeping the source frequency equal to the resonating frequency of the series LCR circuit, if the three elements, L, C and R are arranged in parallel, show that the total current in the parallel LCR circuit is minimum at this frequency. Obtain the current rms value in each branch of the circuit for the elements and source specified in Exercise 7.11 for this frequency.

A circuit containing a 80 mH inductor and a 60 µF capacitor in series is connected to a 230 V, 50 Hz supply. The resistance of the circuit is negligible. (I) Obtain the current amplitude and rmsvalues. (II) Obtain the rms values of potential drops across eachelement. (III) What is the average power transferred to theinductor? (IV) What is the average power transferred to thecapacitor? (V) Whatisthetotalaveragepowerabsorbedbythecircuit?[‘Average’implies ‘averaged over onecycle’.]

Suppose the circuit in Exercise 7.18 has a resistance of 15 ?. Obtain the average power transferred to each element of the circuit, and the total power absorbed.

A series LCR circuit with L = 0.12 H, C = 480 nF, R = 23 ? is connected to a 230 V variable frequency supply. (I) Whatisthesourcefrequencyforwhichcurrentamplitudeismaximum.Obtainthis maximum value. (II) Whatisthesourcefrequencyforwhichaveragepowerabsorbedbythecircuitis maximum. Obtain the value of this maximumpower. (III) Forwhichfrequenciesofthesourceisthepowertransferredtothecircuithalfthe poweratresonantfrequency?Whatisthecurrentamplitudeatthesefrequencies? (IV) What is the Q-factor of the given circuit?

Obtain the resonant frequency and Q-factor of a series LCR circuit with L = 3.0 H, C = 27 µF, and R = 7.4 ?. It is desired to improve the sharpness of the resonance of the circuit by reducing its ‘full width at half maximum’ by a factor of 2. Suggest a suitable way.

A power transmission line feeds input power at 2300 V to a stepdown transformer with its primary windings having 4000 turns. What should be the number of turns in the secondary in order to get output power at 230 V?

At a hydroelectric power plant, the water pressure head is at a height of 300 m and the water flow available is 100 m³ s^-1. If the turbine generator efficiency is 60%, estimate the electric power available from the plant (g= 9.8 m s^-2).

A small town with a demand of 800 kW of electric power at 220 V is situated 15 km away from an electric plant generating power at 440 V. The resistance of the two wire linecarryingpoweris0.5?perkm.Thetowngetspowerfromthelinethrougha4000- 220 V step-down transformer at a sub-station in thetown. (I) Estimate the line power loss in the form ofheat. (II) Howmuchpowermusttheplantsupply,assumingthereisnegligiblepowerlossdue toleakage? (III) Characterise the step up transformer at the plant.

Do the same exercise as above with the replacement of the earlier transformer by a 40,000-220 V step-down transformer (Neglect, as before, leakage losses though this may not be a good assumption any longer because of the very high voltage transmission involved). Hence, explain why high voltage transmission is preferred?