A circuit has an inductance of 1/π H and resistance of 2000 Ω. A 50 Hz A.C. is supplied to it. Calculate the reactance and impedance offered by the circuit. (Ans : `\X_L` = 100 Ω, Z = 2002.5 Ω ) 



Data Given:

Resistance of the Inductance = R =  2000 Ω

Inductance = L = `\frac {1}{ㄫ}` H

Frequency of A.C. supply = f = 50 Hz


To Find:

(i). Inductive Reactance = `\X_L` = ?

(ii). Impedance = Z = ?




Solution:



(i). Inductive Reactance = `\X_L` = ?


Since the Inductive reactance `\X_L` is given by:


`\X_L` = ധL = 2ㄫfL

by putting values


`\X_L`  = ယ L = 2ㄫf L

by putting values

`\X_L`  = 2 ｘ ㄫ ｘ 50 Hz ｘ `\frac {1}{ㄫ}` H 

or

`\X_L`  = 2 ｘ 50 Hz ｘ 1 H 

`\X_L`  = 100 Ω  ---------------Ans. 1



2. Impedance = Z = ?

Z = `\sqrt {R^2 + X_L^2}`

Z = `\sqrt {(2000 Ω)^2 + (100 Ω)^2}`

Z = `\sqrt {4000000 Ω^2 + 10000 Ω^2}`

Z = `\sqrt {4010000 Ω^2}`

Z = 2002.498 Ω

Z = 2002.5 Ω -----------------Ans. (2)





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