A block of metal is heated directly by dissipating power in the internal resistance of block. Because of temperature rise, the resistance increases exponentially with time and is given by R(t) = 0.5 e 2t , where t is in second. The block is connected across a 110 V source and dissipates 7644 J heat energy over a certain period of time. This period of time is...............×10 –1 sec.
Text Solution
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(0005)
Sol. Let t be the required time. As power is
P = 
= 
dU = 
dt
U = 
dt
= 
= (110) 2 (1 – e –2t )J
According to problem,
U = 7644J
Thus 1 – e –2t = 
= 0.632
or e –2t = 0.367
or –2lne = ln 0.367 or –2t = –1 or t = 0.5 s
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