a current of 1.1 A flows through a coil when connected to a 110 V DC source . when 110V -50 Hz AC is applied to the same coil , only 0.5 A current flows . calculate the resistance ,impedance & inductance of the coil.
To calculate the resistance (R), impedance (Z), and inductance (L) of the coil, we can apply Ohm's Law and the concept of reactance.
1. Start by finding the resistance (R) using Ohm's Law:
R = V / I
R = 110 V / 1.1 A
R = 100 Ω
2. Next, we can calculate the impedance (Z) of the coil using the AC current and voltage values:
Z = V / I
Z = 110 V / 0.5 A
Z = 220 Ω
3. To find the inductance (L), we need to first calculate the reactance (X) of the coil using the formula:
X = Z - R
X = 220 Ω - 100 Ω
X = 120 Ω
4. The reactance (X) can be further calculated using the formula:
X = 2πfL
Where f is the frequency (50 Hz) and L is the inductance of the coil. Rearranging the formula, we get:
L = X / (2πf)
L = 120 Ω / (2π * 50 Hz)
L ≈ 0.3828 H (Henry)
Therefore, the resistance is 100 Ω, the impedance is 220 Ω, and the inductance is approximately 0.3828 H.
To calculate the resistance, impedance, and inductance of the coil, we can use the formulas:
Resistance (R) = voltage (V) / current (I)
Impedance (Z) = voltage (V) / current (I)
Inductance (L) = impedance (Z) / angular frequency (ω)
1. Let's start by calculating the resistance using the DC source:
Resistance (R) = 110 V / 1.1 A
= 100 Ω
2. Now, we need to find the impedance using the AC source. However, we need to convert the AC voltage to effective RMS (root mean square) value since it is given as 110V. To do this, we divide it by the square root of 2 (√2):
Effective RMS voltage = 110 V / √2
≈ 77.8 V
Impedance (Z) = effective RMS voltage (V) / current (I)
= 77.8 V / 0.5 A
= 155.6 Ω
3. Finally, we can calculate the inductance using the known angular frequency (ω = 2πf) of 50 Hz:
Angular frequency (ω) = 2π × 50 Hz
= 100π rad/s
Inductance (L) = impedance (Z) / angular frequency (ω)
= 155.6 Ω / (100π rad/s)
≈ 0.494 H
So, the resistance of the coil is approximately 100 Ω, the impedance is approximately 155.6 Ω, and the inductance is approximately 0.494 H.
What is your question about this? It is exceedly straightforward
resistance= dcvoltage/dccurent
impedance=acvoltage/ac current
from those two, you can calulate the inductive reactance (it is a right triangle)
then the inductance is wL=reactance