Question

The tables show the resistance values for three different resistors and the currents through each resistor.
What is the ranking 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

Answer: (D)

$1$ and $3$ tie, $2$

Power dissipated in a resistor is given by ,

$P=I^{2}R$ ,

for $I_1=2I$ , $R_1=R$ ,

$P_1=I_1^2{R}_1$

$P_1=(2I{)}^{2}R=4I^{2}R$ ,

for $I_2=I$ , $R_1=2R$ ,

$P_2=I_2^2{R}_2$

$P_2=I^2\left(2R\right)=2I^{2}R$ ,

for $I_3=I$ , $R_3=4R$ ,

$P_3=I_3^2{R}_3$

$P_3=I^2\left(4R\right)=4I^{2}R$

it is clear that 1 and 3 tie , then 2 .