In the circuit shown- the three voltmeter readings are V1 - 220 V- V2 - 122 V- V3 - 136 V-If RL - 5- - the approximate power consumption in the load is

Given, nbsp; nbsp; R_L = 5Ω nbsp; nbsp; V_S=√((V_1^2+V_2^2+2V_1V_2cosϕ) 220^2=122^2+136^2+2(122)(136)cosϕ cosϕ = 0.45 ∵ cosϕ = R_L | Z | nbsp; ...

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Circuit Theory

Active and Reactive power

In the circui...

Question

In the circuit shown, the three voltmeter readings are $V_{1} = 220 V, V_{2} = 122 V, V_{3} = 136 V .$

If $R_{L} = 5 Ω$ , the approximate power consumption in the load is

700 W

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750 W

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800 W

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850 W

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Solution

The correct option is B 750 W
Given,
$R_{L} = 5 Ω$

$V_{S} = \sqrt{(V_{1}^{2} + V_{2}^{2} + 2 V_{1} V_{2} c o s ϕ}$

$220^{2} = 122^{2} + 136^{2} + 2 (122) (136) c o s ϕ$

$cos ϕ$ = 0.45

$∵ c o s ϕ = \frac{R_{L}}{| Z |}$

$\Rightarrow | Z | = \frac{R_{L}}{c o s ϕ} = \frac{5}{0.45} = 11.11 Ω$

Power consumed by load,

$P_{L} = {(\frac{V_{3}}{| Z |})}^{2} R_{L}$

$= {(\frac{136}{11.11})}^{2} \times 5 = 749.1 ≃ 750 W$

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In the circuit shown, the three voltmeter readings are V1=220V,V2=122V,V3=136V. If RL=5Ω , the approximate power consumption in the load is

The correct option is B 750 WGiven, RL=5Ω VS=√(V21+V22+2V1V2cosϕ 2202=1222+1362+2(122)(136)cosϕ cosϕ = 0.45 ∵ cosϕ=RL|Z| ⇒|Z|=RLcosϕ=50.45=11.11 Ω Power consumed by load, PL=(V3|Z|)2RL =(13611.11)2×5=749.1≃750W

In the circuit shown, the three voltmeter readings are $V_{1} = 220 V, V_{2} = 122 V, V_{3} = 136 V .$

If $R_{L} = 5 Ω$ , the approximate power consumption in the load is