variation of i^² with time t is plotted in the graph for a resistor of resistance 10 ohm. total heat produced in the resistor is
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Answer:
Given, Q=at−bt
2
Current, i=
dt
dQ
=a−2bt
when i=0,a−2bt=0⇒t=t
0
=
2b
a
Thus, current flows from time t=0 to t=t
0
.
The heat produced is:
H=∫
0
t
0
i
2
Rdt
=R∫
0
t
0
[a
2
−4abt+4b
2
t
2
]dt
=R[a
2
t
0
−2abt
0
2
+
3
4b
2
t
0
3
]
=R[a
2
(a/2b)−2ab(a/2b)
2
+
3
4b
2
(a/2b)
3
]
=R[
2b
a
3
−
2b
a
3
+
6b
a
3
]
=
6b
a
3
R
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