CBSE Class 12 Physics 2023 Outside Delhi Set 1 Paper

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Question : 28
Total: 35
A series CR circuit with R=200 and C=(50π) µF is connected across an ac source of peak voltage ε0,=100V and frequency v=50Hz. Calculate (a) impedance of the circuit (Z),(b) phase angle (ϕ), and (c) voltage across the resistor.
(a) Given, R=200,C=
50
π
µ
F

Impedance: Z=R2+(
1
ωC
)
2

Or,
Z=(200)2+(
1
2π×50×
50
π
×106
)
2

Or,
Z=(200)2+(200)2
Z=2002
(b) Phase angle:
θ=tan1
1
ωCR

or, θ=tan1(
1
2π×50×
50
π
×106
×200
)

or, θ=tan11
θ=45
(c) Voltage across resistor:
IRMS=
εRMS
Z

Or, IRMS=
ε0
2
Z

Or, IRMS =
100
2
2002

IRMS=
1
4
A

VR=IRMS ×R
Or, VR=
1
4
×200

VR=50V
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