﻿ The instantaneous current and voltage of an a.c. circuit are given byi = 10 sin 314 t A andv = 50 sin (314 t + π/2)V.What is the power dissipation in the circuit? from Physics Alternating Current Class 12 CBSE

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The instantaneous current and voltage of an a.c. circuit are given by
i = 10 sin 314 t A and
v = 50 sin (314 t + $\mathrm{\pi }$/2)V.
What is the power dissipation in the circuit?

Given,
Instantaneous current, i = 10 sin 314 t A

Instantaneous voltage, V = 50 sin (314 t + $\mathrm{\pi }$/2) V

Since,

Therefore, from the above equations we get

Peak current, peak voltage and $\mathrm{\varphi }$ as,

Power dissipation in the circuit is given by

Therefore,

2248 Views

A 100 volt a.c. source of frequency 500 hertz is connected to LCR circuit with L = 8.1 millihenry, C = 12.5 micro farad and R = 10 ohm, all connected in series. Find the potential difference across the resistance.

Given, an LCR series circuit.
Rms value of voltage, V = 100 V
Frequency = 500 Hz

The impedance of LCR circuit is given by where  and,  = 25.4 ohm Impedence, Rms value of current, Potential difference across resistance 187 Views

A resistance of 10 ohm is joined in series with an inductance of 0.5 henry. What capacitance should be put in series with the combination to obtain the maximum current? What will be the potential difference across the resistance, inductance and capacitor? The current is being supplied by 200 volts and 50 cycles per second mains.

The current in the circuit would be maximum when XL = Xc

i.e.,
Therefore,

Here,
So the impedance Z of the circuit,

Potential difference across resistance

VR = I × R
= 20 × 10
= 200 volt

Potential difference across inductance

Potential difference across condenser

140 Views

An inductor 200 μH, capacitor 500 μF, resistor 10 Ω are connected in series with a 100 V, variable frequency a.c. source. Calculate the
(i) frequency at which the power factor of the circuit is unity
(ii) current amplitude at this frequency
(iii) Q-factor

Given,
Inductor, L = 200 μH
Capacitor, C = 500 μF
Resistor, R = 10 Ω
Effective voltage, V = 100 V

(i) Power factor,

So,

$⇒$

(ii) The current amplitude at this frequency,

(iii) The Q-factor,

351 Views

An LCR series circuit with 100 Ω resistance is connected to an a.c. source of 200 V and angular frequency 300 radians per second. When only the capacitance is removed, the current lags behind the voltage by 60°. When only the inductance is removed, the current leads the voltage by 60°. Calculate the current and power dissipated in LCR circuit.

Given, an LCR series circuit.
Resistance, R = 100 Ω
Rms voltage, V = 200 V
Angular frequency = 300 radians per second.
Current lags behind the voltage by 60o

Using the formula,

or,
$\because$

Impedance of circuit,

Current in the circuit,

Average power,

But,

Now,

590 Views

A resistor of resistance R, an inductor inductance L and a capacitor of capacitance C all are connected in series with an a.c. supply. The resistance of R is 16 ohm and for a given frequency, the inductive reactance of L is 24 ohm and capacitive reactance of C is 12 ohm. If the current in the circuit is 5 amp., find
(a) the potential difference across R, L and C
(b) the impedance of the circuit
(c) the voltage of a.c. supply
(d) phase angle

Given, an LCR circuit where all the components are connected in series with an a.c. supply.
Resistance, R = 16 $\mathrm{\Omega }$
Inductive reactance, ${\mathrm{\chi }}_{\mathrm{L}}$ = 24 ohm
Capacitive reactance,
Current flowing in the circuit, I = 5 A

(a) Potential difference across resistance,
VR = iR
= 5 × 16
= 80 volt

Potential difference across inductance,
VL = i × (ωL)
= 5 × 24
= 120 volt

Potential difference across condenser,

(b) The impedance of the circuit is given as

(c) The voltage of a.c. supply is given by

V = iz
= 5 × 20
= 100 volt

(d) Phase angle

161 Views