Calculating the Equivalent Resistance

To find the equivalent resistance of a parallel combination of a coil with a resistance of 20 Ω and a reactance of 10 Ω, we need to consider the impedance of the coil. Impedance is a complex quantity that incorporates both resistance and reactance.

The impedance of a coil is given by the formula Z = √(R^2 + X^2), where R is the resistance and X is the reactance. Substituting the given values, we have:

Z = √(20^2 + 10^2)
Z = √(400 + 100)
Z = √500
Z ≈ 22.36 Ω

The equivalent resistance of the parallel combination is the reciprocal of the sum of the reciprocals of the individual resistances. In this case, we have:

1/Req = 1/R1 + 1/R2
1/Req = 1/20 + 1/22.36
1/Req ≈ 0.05 + 0.045
1/Req ≈ 0.095

Taking the reciprocal of both sides, we find:

Req ≈ 10.53 Ω

Calculating the Equivalent Reactance

To find the equivalent reactance, we need to consider the impedance of the coil. The reactance of a coil is given by the formula X = Zsin(θ), where Z is the impedance and θ is the phase angle.

In this case, since we have a coil with only a reactance and no resistance, the phase angle is 90 degrees. Thus, we have:

X = Zsin(90)
X = 22.36 * sin(90)
X = 22.36 * 1
X ≈ 22.36 Ω

Therefore, the equivalent reactance of the parallel combination is approximately 22.36 Ω.

Summary

- The impedance of the coil is calculated using the formula Z = √(R^2 + X^2), where R is the resistance and X is the reactance.
- The equivalent resistance of a parallel combination is the reciprocal of the sum of the reciprocals of the individual resistances.
- The equivalent reactance is calculated using the formula X = Zsin(θ), where Z is the impedance and θ is the phase angle.
- In this case, the equivalent resistance is approximately 10.53 Ω and the equivalent reactance is approximately 22.36 Ω.