Question

The impedance of an a.c. circuit is 45 ∠ –30° ohm. The circuit will be

Answer 1

Explanation:

Z=

R

2

+(X

L

−X

C

)

2

∠tan

−1

R

X

L

−X

C

⇒R

2

+(X

L

−X

C

)

2

=100

2

(equation 1)

R

X

L

−X

C

=tan30

o

=

3

1

⇒X

L

−X

C

=

3

R

(equation 2)

Putting equation 2 in 1

R

2

+

3

R

2

=100

2

⇒4R

2

=3×100×100

⇒R

2

=3×25×100

⇒R=86.6Ω

Answer 2

38.97 OHM

Explanation:

We have         $Z = \sqrt (R^2 + (X_L - X_C)^2)\\\\and\\\\\theta = tan^-^1 (\frac{X_L - X_C}{R} )$

Now                $\because \theta =30^0 \ (given)\\\\we \ get \ (X_L - X_C) = \frac{R}{\sqrt 3}$

Finally             $from \ the \ first \ equation,\\\\R^2 + \frac{1}{3} R^2 = 45^2\\\\4R^2 = 6075\\\\R= \sqrt (\frac{6075}{4})\\\\R= 38.9711 \Omega$