Balbharati solutions for Physics [English] 12 Standard HSC Maharashtra State Board chapter 13 - AC Circuits [Latest edition]

Choose the correct option.

If the rms current in a 50 Hz AC circuit is 5A, the value of the current 1/300 seconds after its value becomes zero is ______.

A resistor of 500 Ω and an inductance of 0.5 H are in series with an AC source which is given by V = `100 sqrt2` sin (1000 t). The power factor of the combination is ______.

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In a circuit L, C and R are connected in series with an alternating voltage of frequency f. the current leads the voltage by 45°. The value of C is ______.

In an AC circuit, e and i are given by e = 150 sin(150t)V and i = 150 sin `(150t + π/3)` A. The power dissipated in the circuit is ______.

In a series LCR circuit, the phase difference between the voltage and the current is 45°. Then the power factor will be ______.

An electric lamp is connected in series with a capacitor and an AC source is glowing with a certain brightness. How does the brightness of the lamp change on increasing the capacitance?

Answer in brief.

The total impedance of a circuit decreases when a capacitor is added in series with L and R. Explain why?

Answer in brief.

For a very high-frequency AC supply, a capacitor behaves like a pure conductor. Why?

Answer in brief.

What is wattles current?

Answer in brief.

What is the natural frequency of the LC circuit? What is the reactance of this circuit at this frequency?

In a series LR circuit X_L = R and power factor of the circuit is P₁. When capacitor with capacitance C such that X_L = X_C is put in series, the power factor becomes P₂. Calculate P₁/P₂.

When an AC source is connected to an ideal inductor show that the average power supplied by the source over a complete cycle is zero.

Prove that an ideal capacitor in an AC circuit does not dissipate power

(a) An emf e = e₀ sin ωt applied to a series L - C - R circuit derives a current I = I₀sinωt in the circuit. Deduce the expression for the average power dissipated in the circuit.
(b) For circuits used for transporting electric power, a low power factor implies large power loss in transmission. Explain.

A device Y is connected across an AC source of emf e = e₀ sin ωt. The current through Y is given as i = i₀ sin (ωt + π/2).

1. Identify the device Y and write the expression for its reactance.
2. Draw graphs showing a variation of emf and current with time over one cycle of AC for Y.
3. How does the reactance of the device Y vary with the frequency of the AC? Show graphically.
4. Draw the phasor diagram for device Y.

Derive an expression for the impedance of an LCR circuit connected to an AC power supply. Draw phasor diagram.

Compare resistance and reactance.

Show that in an AC circuit containing a pure inductor, the voltage is ahead of current by π/2 in phase.

An AC source generating a voltage e = e₀sinωt is connected to a capacitor of capacitance C. Find the expression for the current i flowing through it. Plot a graph of e and i versus ωt.

If the effective current in a 50 cycle AC circuit is 5 A, what is the peak value of current? What is the current 1/600 after if was zero?

A light bulb is rated 100W for 220 V AC supply of 50 Hz. Calculate

1. resistance of the bulb.
2. the rms current through the bulb

A 15.0 μF capacitor is connected to a 220 V, 50 Hz source. Find the capacitive reactance and the current (rms and peak) in the circuit. If the frequency is doubled, what will happen to the capacitive reactance and the current?

An AC circuit consists of only an inductor of inductance 2 H. If the current is represented by a sine wave of amplitude 0.25 A and frequency 60 Hz, calculate the effective potential difference across the inductor. (π = 3.142)

Alternating emf of e = 220 sin 100 πt is applied to a circuit containing an inductance of (1/π) henry. Write an equation for instantaneous current through the circuit. What will be the reading of the AC galvanometer connected in the circuit?

A 25 μF capacitor, a 0.10 H inductor, and a 25Ω resistor are connected in series with an AC source whose emf is given by e = 310 sin 314 t (volt). What is the frequency, reactance, impedance, current, and phase angle of the circuit?

A capacitor of 100 μF, a coil of resistance 50Ω, and an inductance 0.5 H are connected in series with a 110 V-50Hz source. Calculate the rms value of current in the circuit.

Find the capacity of a capacitor which when put in series with a 10Ω resistor makes the power factor equal to 0.5. Assume an 80V-100Hz AC supply.

Find the time required for a 50 Hz alternating current to change its value from zero to the rms value.

Calculate the value of the capacity in picofarad, which will make 101.4 microhenry inductance to oscillate with a frequency of one megahertz.

A 10 μF capacitor is charged to a 25 volt of potential. The battery is disconnected and a pure 100 m H coil is connected across the capacitor so that LC oscillations are set up. Calculate the maximum current in the coil.

A 100 μF capacitor is charged with a 50 V source supply. Then source supply is removed and the capacitor is connected across an inductance, as a result of which 5A current flows through the inductance. Calculate the value of the inductance.