Given,
C=10 μF
R=20 Ω
V=20 V
We know, current in an RC circuit is given by
i=VRe(−tRC)
Power dissipated by the resistor is given by
PR=i2R=⎛⎜⎝VRe(−tRC)⎞⎟⎠2R=V2Re⎛⎝−2tRC⎞⎠
Energy consumed by the resistor ER=∫∞0PRdt
ER=∫∞0V2Re⎛⎝−2tRC⎞⎠ dt
ER=V2R∫∞0 e⎛⎝−2tRC⎞⎠ dt
ER=V2RCR2|e0−e∞|=12CV2
ER=12×10×10−6×202=2×10−3J=2 mJ
Energy consumed by resistor alone is equal to 2 mJ
∴ Energy supplied by battery must be >2 mJ
Hence, the correct answer is OPTION C.