Q.2 The resistance of a wire is 100
Ohms. If it carries a current of 1 A for
10 seconds, the heat produced will
be..........
O 1000 J
O 100
J
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12th
Physics
Alternating Current
AC Voltage Applied to an Resistor
A resistor of resistance 1...
PHYSICS
A resistor of resistance 100ohm is connected to an AC
source =(12V) sin(250πs
−1
)t. Find the energy dissipated as heat during t=0 to t=1.0ms
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ANSWER
Given :
the peak voltage of AC source E
0
=12V
Angular frequency, ω=250πs
−1
The resistance of the resistor, R=100Ω
The energy dissipated as heat (H)is given by,
H=
R
E
rms
T
here, E
rms
= RMS value of voltage
R= Resistance of the resistor
T=temperature
Energy dissipated as heat during t=0 to t=1.0 ms,
H=∫
0
10
−3
dH
=∫
R
E
0
2
sin
2
wt
dt(sinceE
Rms=E
0
sin wt
)
=
100
144
∫
0
10
−3
(sin
2
wt)dt
1.44∫
0
10
−3
(
2
1−cos2wt
)dt
=
2
1.44
[∫
10
0
−3
dt+∫
0
10
−3
cos2wt dt]
=0.72[10
−3
−(
2w
sin2wt
)
0
10
−3
]
=0.72[
100
1
−
500π
1
]
=0.72[
1000
1
−
500π
1
]
=0.72[
1000
1
−
1000π
2
]
=(
1000π
π−2
)×0.72
=0.0002614=2.61]×10
−4
J
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