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 $Q,H_Q=I_1^{2}Qt=\frac{I_2^2}{4}\times 4t=I_2^{2}t$
For $S,H_S=I_2^{2}St=I_2^2\cdot 2t=2I_2^{2}t$
$\therefore$ Greatest amount of heat generated by $S$