Questions

Current in an ac circuit is given by$I=3\mathrm{sin}\omega t+4\mathrm{cos}\omega t$, then

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a

rms value of current is 5 A.

b

mean value of this current in any one half period will be 6/π

c

if voltage applied is V=Vmsinωt, then the circuit may be containing resistance and capacitance only.

d

if voltage applied rs V=Vmsinωt the circuit may contain resistance and inductance only.

detailed solution

Correct option is C

i=3 sin ωt+4 cos ωt=535 sin ωt+45 cos ωt=5sin ωt+δ ......irms value = 52AMean value=2πi0=10πAIf voltage applied is V=Vm sin ωt then I, given by Eq. (i), indicates that it is ahead of V by δ where 0 < δ < 90 whichindicates that the circuit contains R and C.If we find average value for the first half period (0 to T/2), then it will be 6π/A. But for different time interval, it will bedifferent.

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