Advertisements
Advertisements
प्रश्न
A series RL circuit with R = 10 Ω and L = `(100/pi)` mH is connected to an ac source of voltage V = 141 sin (100 πt), where V is in volts and t is in seconds. Calculate
- the impedance of the circuit
- phase angle, and
- the voltage drop across the inductor.
Advertisements
उत्तर
Given:
R = 10 Ω
L = `(100/pi)` mH
V = 141 sin (100 π)t
From this equation, we get the value of ω = 100π and V = 141 volt
- To find: Impedance (Z)
Z = `sqrt(R^2 + X_L^2)`
Where Z is the impedance, R is the resistance, and XL is the impedance,
XL = ωL
XL = `(100pi xx 100)/(pi xx 10^-3)`
XL = 10Ω
Z = `sqrt(R^2 + X_L^2)`
Z = `sqrt((10)^2 + (10)^2)`
Z = `sqrt200`
Z = `10sqrt2`Ω - Phase Angle (Φ):
We can calculate the phase angle by the following formula,
`cosphi = R/Z`
`cosphi = 10/(10sqrt2)`
`cosphi = 1/sqrt2`
`phi = 45^circ` - Voltage drop:
`V_L = IX_L`
= `V/Z xx X_L`
`V_L = 141/(10sqrt2) xx 10`
`V_L = 141/sqrt2`
`V_L ≅ 100` volt
APPEARS IN
संबंधित प्रश्न
An inductor of inductance 2.00 H is joined in series with a resistor of resistance 200 Ω and a battery of emf 2.00 V. At t = 10 ms, find (a) the current in the circuit, (b) the power delivered by the battery, (c) the power dissipated in heating the resistor and (d) the rate at which energy is being stored in magnetic field.
Two coils A and B have inductances 1.0 H and 2.0 H respectively. The resistance of each coil is 10 Ω. Each coil is connected to an ideal battery of emf 2.0 V at t = 0. Let iA and iBbe the currents in the two circuit at time t. Find the ratio iA / iB at (a) t = 100 ms, (b) t = 200 ms and (c) t = 1 s.
The potential difference across the resistor is 160V and that across the inductor is 120V. Find the effective value of the applied voltage. If the effective current in the circuit be 1.0 A, calculate the total impedance of the circuit.
In a series, LCR circuit, obtain an expression for the resonant frequency.
A series LCR circuit with L = 0.12 H, C = 480 nF, R = 23 Ω is connected to a 230 V variable frequency supply.
(a) What is the source frequency for which current amplitude is maximum. Obtain this maximum value.
(b) What is the source frequency for which average power absorbed by the circuit is maximum. Obtain the value of this maximum power.
(c) For which frequencies of the source is the power transferred to the circuit half the power at resonant frequency? What is the current amplitude at these frequencies?
(d) What is the Q-factor of the given circuit?
In series combination of R, L and C with an A.C. source at resonance, if R = 20 ohm, then impedence Z of the combination is ______.
In a series LCR circuit the voltage across an inductor, capacitor and resistor are 20 V, 20 V and 40 V respectively. The phase difference between the applied voltage and the current in the circuit is ______.
To reduce the resonant frequency in an LCR series circuit with a generator
In series LCR AC-circuit, the phase angle between current and voltage is
The net impedance of circuit (as shown in figure) will be ______.
