Question

The table below show the resistance values for three different resistors and the currents through each resistor. What is the ranking order of the power dissipated by each resistor, greatest first.

Current 1	2I
Resistance 1	R
Current 2	I
Resistance 2	2R
Current 3	I
Resistance 3	4R

• A. 3, 2 and 1 tie
• B. 3, 2, 1
• C. 1, 2, 3
• D. 1 and 3 tie, 2
• E. all tie

Answer 1

The correct option is D 1 and 3 tie, 2

Given : $I_1=2I$, $R_1=R$ $I_2=I$ , $R_2=2R$ $I_3=I$, $R_3=4R$

Power dissipated across $R_1$, $P_1=I_1^2{R}_1=(2I{)}^2\times R=4I^{2}R$

Power dissipated across $R_2$, $P_2=I_2^2{R}_2=I^2\times \left(2R\right)=2I^{2}R$

Power dissipated across $R_3$, $P_3=I_3^2{R}_3=I^2\times \left(4R\right)=4I^{2}R$

$⟹$ $P_1=P_3>P_2$

Hence option D is correct.