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.
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
Find the value of t/τ for which the current in an LR circuit builds up to (a) 90%, (b) 99% and (c) 99.9% of the steady-state value.
An inductor-coil of inductance 17 mH is constructed from a copper wire of length 100 m and cross-sectional area 1 mm2. Calculate the time constant of the circuit if this inductor is joined across an ideal battery. The resistivity of copper = 1.7 × 10−8 Ω-m.
Consider the circuit shown in figure. (a) Find the current through the battery a long time after the switch S is closed. (b) Suppose the switch is again opened at t = 0. What is the time constant of the discharging circuit? (c) Find the current through the inductor after one time constant.
Use the expression for Lorentz force acting on the charge carriers of a conductor to obtain the expression for the induced emf across the conductor of length l moving with velocity v through a magnetic field B acting perpendicular to its length.
Derive an expression for the average power dissipated in a series LCR circuit.
In an LCR series a.c. circuit, the voltage across each of the components, L, C and R is 50V. The voltage across the LC combination will be ______.
A series LCR circuit contains inductance 5 mH, capacitance 2µF and resistance ion. If a frequency A.C. source is varied, what is the frequency at which maximum power is dissipated?
To reduce the resonant frequency in an LCR series circuit with a generator
A series LCR circuit containing a resistance of 120 Ω has angular resonance frequency 4 × 105 rad s-1. At resonance the voltage across resistance and inductance are 60 V and 40 V respectively. At what frequency the current in the circuit lags the voltage by 45°. Give answer in ______ × 105 rad s-1.
A series LCR circuit is connected to an ac source. Using the phasor diagram, derive the expression for the impedance of the circuit.
