Question

(a) State and explain joule's law of heating.
(b) A resistance of 40 ohms and one of 60 ohms are arranged in series across 220 volts find heat in joules produced by this combination of resistance in half a minute.

Answer 1

a) When current I flow through a resistor of electric resistance R, heat is produced. The heat produced H depends directly on the square of the current, resistance and time t for which the current is allowed to pass.
$H=I^{2}Rt$, Is called Joule’s law of heating.

SI unit Heat energy: joule

b) Let R1 = 40 ohm
R2 = 60 ohm
According to the question ,
R1 and R2 are in series combination,
so, equivalent Resistance (Req) = R1 + R2
Req = 40 + 60 = 100 ohm

now , we know ,
$Heat=I^{2}Rt$
also , $V=IR$ ( according to ohm' s law )
$Heat=(\frac{V}{R}{)}^2\times R\times t$
$=V²\times \frac{t}{R}$

here,
Req = R = 100 ohm
V = 220 volt
t = 30 sec
then,
$Heat=(220{)}^2\times 30/100J$
= $=48400\times 30/100J$
= $=484\times 30J$
= 14520 Joule

hence, heat = 14520 Joule