A coil has a resistance of 10 - and an inductance of 0-4 henry- It is connected to an AC source of 6-5 V - 30- Hz- Find the average power consumed in the circuit-

Given R = 10 W, L = 0.4 Henry, E = 6.5 V, f= 30/π H_2 Z = √(R^2+ X^2_L) = √(R^2+ (2πfL)^2) Power = V_rms I_rms cos θ = 6.5 ×6.5/ZR/Z = 6.5 × 6.5 × 10/ [ √(r ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Power in an AC Circuit

A coil has a ...

Question

A coil has a resistance of $10 Ω$ and an inductance of 0.4 henry. It is connected to an AC source of 6.5 V, $\frac{30}{π}$ Hz. Find the average power consumed in the circuit.

Open in App

Solution

Given R = 10 W,

L = 0.4 Henry,

E = 6.5 V,

f= $\frac{30}{π} H_{2}$

Z = $\sqrt{R^{2} + X_{L}^{2}}$

= $\sqrt{R^{2} + (2 π f L)^{2}}$

Power = $V_{r m s} I_{r m s} c o s θ$

= $6.5 \times \frac{6.5}{Z} \frac{R}{Z}$

= $\frac{6.5 \times 6.5 \times 10}{{[\sqrt{r^{2}} + (2 π f L)^{2}]}^{2}}$

= $\frac{6.5 \times 6.5 \times 10}{(10)^{2} + (2 π . \frac{30}{π} .0 .4)^{2}}$

= $\frac{6.5 \times 6.5 \times 10}{100 + 576}$

= $\frac{6.5 \times 6.5 \times 10}{676}$

= 0.625 = $\frac{5}{8}$ W

Suggest Corrections

Similar questions

Q. A coil has a resistance of

10 Ω

and an inductance of

0.4 H

. It is connected across an AC source of

6.5 V, \frac{30}{π} Hz

. The average power consumed in the circuit is

Q. A circuit, containing an inductance and a resistance connected in series, has an AC source of

200 V, 50 Hz

connected across it. An AC rms current of

10 A

flows through the circuit and the power loss is measured to be

1 kW

. Then

Q. An

A C

source of emf

E = 200 sin [100 t] V

is connected to a choke coil of inductance

1 H

and resistance

100 Ω

. Find the average power consumed.

Q. A resistance is connected to an AC source. If a capacitor is included in the series circuit, will the average power absorbed by the resistance increase or decrease? If an inductor of small inductance is also included in the series circuit, will the average power absorbed increase or decrease further?

Q. A coil has resistance of

6 Ω

& inductance of

0.08 H

. It is connected with alternating voltage of

250 V, \frac{50}{π} H z .

The average power consumed in circuit

Join BYJU'S Learning Program

A coil has a resistance of 10Ω and an inductance of 0.4 henry. It is connected to an AC source of 6.5 V, 30π Hz. Find the average power consumed in the circuit.

Given R = 10 W, L = 0.4 Henry, E = 6.5 V, f= 30πH2 Z = √R2+X2L = √R2+(2πfL)2 Power = VrmsIrmscos θ = 6.5×6.5ZRZ = 6.5×6.5×10[√r2+(2πfL)2]2 = 6.5×6.5×10(10)2+(2π.30π.0.4)2 = 6.5×6.5×10100+576 = 6.5×6.5×10676 = 0.625 = 58 W

A coil has a resistance of $10 Ω$ and an inductance of 0.4 henry. It is connected to an AC source of 6.5 V, $\frac{30}{π}$ Hz. Find the average power consumed in the circuit.