Question

The impedance of an AC circuit is 45∠–30° Ω. The circuit will be ________

Answer 1

Answer:

Z= R 2 +(X L −X C ) ∠tan −1 RX L −X C

⇒R 2+(X L −X C ) =100 2

(equation 1)

RX L−X C =tan30 o = 31

⇒X L −X C

= 3R

(equation 2)

Putting equation 2 in 1

R 2+ 3R 2

=100 2

⇒4R

2

=3×100×100

⇒R

2

=3×25×100

⇒R=86.6Ω

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Answer 2

Given:

The impedance of an AC circuit is 45∠-30°Ω

To Find:

The circuit will be of what resistance.

Solution:

Impedance is the measure of the opposition that a circuit presents to a current when voltage is applied.

It is the ratio to the voltage or current.

It is a complex number with the same unit of resistance and SI unitΩ.

Now,

Z = $\sqrt{R^{2}+(X_{L}-X_{C})^{2} }$∠$tan^{-1}\frac{X_{L}-X_{C} }{R}$

Z is used to represent impedance

The above equation can be further written as,

⇒ R² +($X_{L}-X_{C}$)² = 100² ..(i)

Then putting the value of tan30

$\frac{X_{L}_X_{C} }{R}$ = tan30° = 1/√3

$X_{L}-X_{C}=\frac{R}{\sqrt{3} }$ ..(ii)

Now, putting (ii) in (i),

R²+R²/3 = 100²

⇒ 4R² = 3 × 100 × 100

⇒ R² = 3 × 25 × 100

⇒ R = 86.6Ω

Therefore, the circuit will be 86.6Ω