Question

Which of the four resistances $P, Q, R$ and $S$ generate the greatest amount of heat when a current flows from $A$ to $B$ ?

• A. $Q$
• B. $S$
• C. $P$
• D. $R$

Answer 1

Answer: (B)

$R_{1}=P+Q=2\,\Omega+4\,\Omega =6\,\Omega$
$R_{2}=R+S=1\Omega+2\,\Omega =3\,\Omega$
$I_{1}R_{1}=I_{2}R_{2}$
$I_{1}=\frac{R_{2}}{R_{1}}I_{2}=\frac{3}{6}I_{2}-\frac{I_{2}}{2}$
or $I_{2}=2I_{1}$
Heat flow $H = I^{2}Rt$
For $Q, H_{Q}=I^{2}_{1}\,Qt=\frac{I^{2}_{2}}{4}\times4t=I^{2}_{2}t$
For $S, H_{S}=I^{2}_{2}\,St=I^{2}_{2}\cdot2t=2I^{2}_{2}t$
$\therefore $ Greatest amount of heat generated by $S$