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 Multiple Choice QuestionsMultiple Choice Questions

111.

In the given circuit, the AC source has ω = 100 rad/s, considering the inductor and capacitor to be ideal,

    

  • the current through the circuit  is 0.4 A

  • the current through the circuit is 0.32 A

  • the voltage across 100 Ω  resistor is 102 V

  • the voltage across 50 Ω resistor is 10 V


C.

the voltage across 100 Ω  resistor is 102 V

In R-C circuit

Z = R2 + Xc2   = 1002 + 1100 × 100 × 10-62    = 1002 + 1002   = 1002 ΩCurrent in this branch, i1 = 201002 = 152 ACurrent leads voltage  tan ϕ = XCR = 1 by π4In R-L circuit,   Z = R2 + XL2      = 502 + 100 × 52      = 502 ΩCurrent in this branch, i2 = 20502 = 252 A


112.

An inductor 20 mH, a capacitor 100 µF and a resistor 50 Ω are connected in series across a source of emf, V = 10 sin 314 t. The power loss in the circuit is

  • 0.79 W

  • 0.43

  • 1.13

  • 2.74 W


A.

0.79 W

Power dissipated in an LCR series connected to an a.c source of emf E

P = Ermsirms cosϕ = E2rmsRZ2 = Erms2 RR2+ωL-1Cω2=1022 x 50(50)2 +314 x 20 x 10-3 - 1314 x 100 x 10-62solving we get, P = 0.79 W


113.

Given,

R1 = 10 Ω, C1 = 2µF, R2 = 20 and C2 =  4F

The time constants (in µs) for the circuits I, II, III are respectively.

  • 18, 18/9, 4

  • 4, 8/9, 18

  • 18, 4, 8/9

  • 8/9, 18, 4


D.

8/9, 18, 4

Time constant, ζ =  RC            ζ1 = RC = 1 × 21 + 2 × 2 × 42 + 4                 = 23 × 86 = 89 μs             ζ2 = 1 + 2 2 + 4                 = 3 × 6 = 18μs             ζ3 = 1 × 21 + 2 2 + 4                 = 23 × 6                 = 4 μs