Question
The three resistance of equal value are arranged in the different combinations shown below. Arrange them in increasing order of power dissipation.
The three resistance of equal value are arranged in the different combinations shown below. Arrange them in increasing order of power dissipation.
A.
$$III < II < IV < I$$
B.
$$II < III < IV < I$$
C.
$$I < IV < III < II$$
D.
$$I < III < II < IV$$
Answer :
$$III < II < IV < I$$
Solution :
III < II < IV < I.
Power dissipation, $${P_1} = {I^2}\left( {3R} \right) = 3{I^2}R$$
Power dissipation, $${P_2} = {I^2}\left( {\frac{{2R}}{3}} \right) = 0.67{I^2}R$$
Power dissipation, $${P_3} = {I^2}\left( {\frac{R}{3}} \right) = 0.33{I^2}R$$
Power dissipation, $${P_4} = {I^2}\left( {\frac{3}{2}R} \right) = 1.5{I^2}R$$
III < II < IV < I.
Power dissipation, $${P_1} = {I^2}\left( {3R} \right) = 3{I^2}R$$
Power dissipation, $${P_2} = {I^2}\left( {\frac{{2R}}{3}} \right) = 0.67{I^2}R$$
Power dissipation, $${P_3} = {I^2}\left( {\frac{R}{3}} \right) = 0.33{I^2}R$$
Power dissipation, $${P_4} = {I^2}\left( {\frac{3}{2}R} \right) = 1.5{I^2}R$$
