Q24 of 30 Page 1

(a) Write the mathematical expression for Joule's law of heating.

(b) Compute the heat generated while transferring 96000 coulomb of charge in two hours through a potential difference of 40 V.


The amount of work done when an electric charge, move against a potential difference which is denoted by V is given by;

W=V x Q …….. (1)


From the above expression,



We know that,


V=IR …….. (2)


Q=It …… (3)


Therefore,



Let us substitute (2) and (3) in (1) we get,


W=(IR)(It)


W=H


Where H is the amount of heat produced, it is expressed in Joules J and I is expressed in terms of Ampere.


Therefore, we can write


H = I2Rt


(b) Given


Charge given, Q = 96000 C


Time given (t) = 2 hour = 2 × 60 × 60 s =7200 s


Voltage (V) = 40 V


We know that, current can be found out by using the formula,




Amount of heat generated can be found out using the formula,



Thus, the “amount of heat” generated is 3840 kJ


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