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
Inductive reactance, = 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
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,
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,
Impedance of circuit,
Current in the circuit,
Average power,
But,
Now,