Question : An ac source V=282sin(100t) volt is connected across a 1µF capacitor. The rms value of current in the circuit will be (take √2=1.41)
(A) 10 mA
(B) 20 mA
(C) 40 mA
(D) 80 mA
Doubt by Japjee
Solution :
Solution :
V=282sin(100t) volt
On comparing with
V=V₀Sinωt
V₀=282 Volt
ω=100 rad/s
On comparing with
V=V₀Sinωt
V₀=282 Volt
ω=100 rad/s
C=1µF
=1×10-6F
XC=1/ωC
XC=1/[100×1×10-6]
XC=1/10-4
XC=104 Ω
Now,
V₀=I₀XC
I₀=V₀/XC
I₀=282/104
√2×Irms = 282/104 [∵Irms=I₀/√2]
Irms = 282/[104×√2]
Irms = 282/[104×1.41]
Irms = 282/14100
Irms = 2/100
Irms = 2×10-2
Irms = 20×10-2
Irms = 20 mA
=1×10-6F
XC=1/ωC
XC=1/[100×1×10-6]
XC=1/10-4
XC=104 Ω
Now,
V₀=I₀XC
I₀=V₀/XC
I₀=282/104
√2×Irms = 282/104 [∵Irms=I₀/√2]
Irms = 282/[104×√2]
Irms = 282/[104×1.41]
Irms = 282/14100
Irms = 2/100
Irms = 2×10-2
Irms = 20×10-2
Irms = 20 mA
Hence, (B) 20 mA, would be the correct option.
