Question

) A coil of resistance 10Ω and inductance 0.02H is connected in series with another coil of

resistance 6Ω and inductance 15mH across a 230 V, 50Hz supply. Calculate ________________ [6]

(i) Impedance of the circuit.

(ii) Voltage drop across each coil.

(iii) The total power consumed by the circuit​

Answer 1

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Answer 2

Given:

Two coils of resistances 10Ω and 6Ω and inductances 0.02H and 15mH respectively are connected in series with a 230V, 50Hz supply.

To Find:

• Impedance of the circuit.
• Voltage drop across each coil.
• The total power consumed by the circuit.

Solution:
Here, the net resistance of the circuit, $R=R_1+R_2=16$Ω

The net inductance of the circuit, $L=L_1+L_2=0.035H$

The reactance offered by the inductors combined, $X_L=2\pi fL$

                                                                                         $=2*3.14*50*0.035$

                                                                                         $=11$Ω

The total impedance of an RL circuit is given by, $Z=\sqrt{R^2+X_L^2}$

                                                                                    $=\sqrt{(16)^2+(0.035)^2}$

                                                                                    $=19.4$Ω

Current through the circuit, $I=\frac{V}{Z}$

                                                $=\frac{230}{19.4}$

                                                $=11.86A$

The impedance of the first coil, $Z_1=\sqrt{R_1^2+X_{L_1}^2}=\sqrt{10^2+(2\pi *50*0.02)^2}$

                                                   $=11.8$Ω.

Similarly, we can find $Z_2=7.62$Ω

The voltage drop across the first coil,  $V_1=IZ_1=140V$

The voltage drop across the second coil, $V_2=IZ_2=90V$

Power consumed by the coil, $P=VI$cosφ,

where cosφ$=\frac{R}{Z}$ is the power factor of the ac circuit.

$P=230*11.86*\frac{16}{19.4}=2250W$.

Hence the impedance if the circuit is 19.4Ω, the voltage drop across the first coil and the second coils are 140V and 90V respectively and the power consumed by the circuit is 2250W.