A series circuit consists of a resistance- inductor and capacitance- The applied voltage and the current at any instant are given by E - 141-4 cos5000 t -10- V and I -5 cos5000 t -370- A- The inductance of inductor is 0-01 H- Calculate the value of capacitance-A- 1 - FB- 6 - FC- 4 - FD- 5 - F

Impedance of circuit Z=EI_0=100√(2)5=20√(2) tanϕ = X_L X_CR Phase difference between E and I is ϕ = 2 π i.e tan ϕ = X_L X_CR=0 ⇒ X_L=X_C ⇒ω L = 1ω C ∴ω^2 =1LC ...

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Byju's Answer

Standard XII

Physics

Impedance in RLC Circuit

A series circ...

Question

A series circuit consists of a resistance, inductor and capacitance. The applied voltage and the current at any instant are given by $E = 141.4 cos (5000 t - 10^{\circ}) V$ and $I = 5 cos (5000 t - 370^{\circ}) A$ . The inductance of inductor is $0.01 H$ . Calculate the value of capacitance.

5 μ F

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1 μ F

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4 μ F

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6 μ F

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Solution

The correct option is C $4 μ F$
Impedance of circuit $Z = \frac{E}{I_{0}} = \frac{100 \sqrt{2}}{5} = 20 \sqrt{2}$
$tan ϕ = \frac{X_{L} - X_{C}}{R}$
Phase difference between $E$ and $I$ is
$ϕ = 2 π$
i.e $tan ϕ = \frac{X_{L} - X_{C}}{R} = 0$
$\Rightarrow X_{L} = X_{C} \Rightarrow ω L = \frac{1}{ω C}$
$∴ ω^{2} = \frac{1}{L C}$

From equation of $E$ and $I$
$ω = 5000$
and given $L = 0.01 H$
$\Rightarrow C = \frac{1}{0.01 (5000)^{2}} = 4 μ F$

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A series circuit consists of a resistance, inductor and capacitance. The applied voltage and the current at any instant are given by E=141.4cos(5000t–10∘)V and I=5cos(5000t–370∘) A. The inductance of inductor is 0.01 H. Calculate the value of capacitance.

The correct option is C 4 μFImpedance of circuit Z=EI0=100√25=20√2 tanϕ=XL−XCR Phase difference between E and I is ϕ=2π i.e tan ϕ=XL−XCR=0 ⇒XL=XC⇒ωL=1ωC ∴ω2=1LC From equation of E and I ω=5000 and given L=0.01 H ⇒C=10.01(5000)2=4 μF

A series circuit consists of a resistance, inductor and capacitance. The applied voltage and the current at any instant are given by $E = 141.4 cos (5000 t - 10^{\circ}) V$ and $I = 5 cos (5000 t - 370^{\circ}) A$ . The inductance of inductor is $0.01 H$ . Calculate the value of capacitance.