In the diagram above, the ratio of he electric power dissipated in the 6Ω and the 3Ω resistor respectively is
A. 2:1
B. 2:2
C. 1:3
D. 1:2
Correct Answer: D
Explanation
Power, P = I
2R;
and I =
E/
RBut effective Parallel resistance: is given by:
1/
R =
1/
6 +
1/
3 =
1+2/
6 =
3/
6 => R =
6/
3 = 2Ω
Current I =
E/
R =
12/
2 = 6A
But I
1 = (
R1/
R[sub]1+R
2[/sub]) x 1 =
3/
9 x 6 = 2A
again I
1 = (
R1/
R[sub]1+R
2[/sub]) x 1 =
6/
9 x 6 = 4A
∴P
1 = I
12 R
1 = 2 x 2 x 6 = 24W
P
2 = I
22 R
2 = 4 x 4 x 3 = 48W
thus
P1/
P[sub]2[/sub] =
24/
48 =
1/
2 ; OR P
1 : P
2 = 1:2
