Question

Two coils are connected in series having resistance and inductive reactance 5 and 6 ohm, 3 and 7ohm respectively. A sinusoidal voltage of 200V, 50Hz is applied across the combination. Calculate (i) current, pf and power absorbed in the whole ckt.
(ii)Voltage drop across each coil
(iii)Power factor and power absorbed in each coil.​

Answer 1

Explanation:

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Answer 2

Answer:

(i) Current -13.28A, Power factor-0.73,Power absorbed-1938.88W

(ii)Voltage drops are 77.42V and 122.44 V.

(iii)Power factor for the coils- 0.85 and 0.65, Power absorbed by the coils-873.9 W and 1056.90W.

Explanation:

First, we need to find impedance (Z)of the individual circuit and then we will add them to get total impedance(ZT).

We know that,

$Z=\sqrt{R^2+X_L^2}$

The values given in the question are,

R₁=5Ω

R₂=6Ω

XL₁=3Ω

XL₂=7Ω

V=200v

Frequency=50Hz

$Z_1=\sqrt{5^2+3^2} =5.83\Omega$

$Z_2=\sqrt{6^2+7^2} =9.22\Omega$

$Z_T=Z_1+Z_2$

$Z_T=5.83+9.22=15.05\Omega$

(i) $Current(I)=\frac{voltage}{Z_T}$                      (1)

$I=\frac{200}{15.05}=13.28A$

$Power factor(cos\theta)=\frac{R_T}{Z_T}$                     (2)

RT=5Ω+6Ω=11Ω

$cos\theta=\frac{11}{15.05}=0.73$                         (3)

Power absorbed in the whole circuit(P)=VIcosθ       (4)

By substituting the values of V, I, and cosθ in equation (4) we get;

$P=200\times13.28\times0.73=1938.88 W$       (5)

(ii)

The voltage drop across the first circuit(V₁)=I×Z₁       (6)

$V_1=13.28\times5.83=77.42V$

The voltage drop across the second circuit(V₂)=I×Z₂     (7)

$V_2=13.28\times9.22=122.44V$

(iii)

For the first coil

Power factor(cosθ₁)=R₁/Z₁            (8)

$cos\theta_1=\frac{5}{5.83}=0.85$

Power absorbed (P₁)=V₁Icosθ₁        (9)

$P_1=77.42\times\ 13.28\times 0.85=873.9W$

For the second coil

Power factor(cosθ₂)=R₂/Z₂            (10)

$cos\theta_2=\frac{6}{9.22}=0.65$

Power absorbed (P₂)=V₂Icosθ₂    (11)

$P_2=122.44\times 13.28\times 0.65=1056.90W$

Hence, The current absorbed in the circuit is 13.28A, the power factor of the whole circuit is 0.73, power absorbed in the whole circuit is 1938.88W, respective voltage drops across the circuit is 77.42V and 122.44 V respectively, respective power factor and power absorbed in each coil is 0.85 and 0.65,873.9 W and 1056.90W respectively.