Published by:
CGP EDU Academic Team
Published on: September 12, 2026
Arrange the order of power dissipated in the given circuits, if the same current is passing through the system. The resistance of each resistor is ' r '.
(i) 
(ii) 
(iii) 
(iv) 
Text Solution
Verified by ExpertsThe correct answer is:
A
To determine the power dissipated in each circuit with the same current, we apply the formula for power:
$$ P = I^2 R $$
Since the current (I) is constant in all circuits, we need to calculate the equivalent resistance (R) for each configuration to compare the power.
1. **Circuit (i)**: Two resistors in series. The equivalent resistance \( R_1 \) is:
$$ R_1 = r + r = 2r $$
Power: $$ P_1 = I^2 R_1 = I^2 (2r) = 2I^2 r $$
2. **Circuit (ii)**: Four resistors in series. The equivalent resistance \( R_2 \) is:
$$ R_2 = r + r + r + r = 4r $$
Power: $$ P_2 = I^2 R_2 = I^2 (4r) = 4I^2 r $$
3. **Circuit (iii)**: Two pairs of resistors in parallel, where each pair is in series. Each pair's resistance is \( r \), and they are in parallel:
$$ R_3 = \frac{r}{2} $$
Power: $$ P_3 = I^2 R_3 = I^2 \left( \frac{r}{2} \right) = \frac{I^2 r}{2} $$
4. **Circuit (iv)**: Two resistors in parallel. Equivalent resistance \( R_4 \) is:
$$ R_4 = \frac{r}{2} $$
Power: $$ P_4 = I^2 R_4 = I^2 \left( \frac{r}{2} \right) = \frac{I^2 r}{2} $$
Now we compare the powers:
- \( P_2 = 4I^2 r \) (highest)
- \( P_1 = 2I^2 r \)
- \( P_4 = \frac{I^2 r}{2} \)
- \( P_3 = \frac{I^2 r}{2} \)
Therefore, the order of power dissipated is:
**P2 > P1 > P4 = P3**, which corresponds to Option A.
$$ P = I^2 R $$
Since the current (I) is constant in all circuits, we need to calculate the equivalent resistance (R) for each configuration to compare the power.
1. **Circuit (i)**: Two resistors in series. The equivalent resistance \( R_1 \) is:
$$ R_1 = r + r = 2r $$
Power: $$ P_1 = I^2 R_1 = I^2 (2r) = 2I^2 r $$
2. **Circuit (ii)**: Four resistors in series. The equivalent resistance \( R_2 \) is:
$$ R_2 = r + r + r + r = 4r $$
Power: $$ P_2 = I^2 R_2 = I^2 (4r) = 4I^2 r $$
3. **Circuit (iii)**: Two pairs of resistors in parallel, where each pair is in series. Each pair's resistance is \( r \), and they are in parallel:
$$ R_3 = \frac{r}{2} $$
Power: $$ P_3 = I^2 R_3 = I^2 \left( \frac{r}{2} \right) = \frac{I^2 r}{2} $$
4. **Circuit (iv)**: Two resistors in parallel. Equivalent resistance \( R_4 \) is:
$$ R_4 = \frac{r}{2} $$
Power: $$ P_4 = I^2 R_4 = I^2 \left( \frac{r}{2} \right) = \frac{I^2 r}{2} $$
Now we compare the powers:
- \( P_2 = 4I^2 r \) (highest)
- \( P_1 = 2I^2 r \)
- \( P_4 = \frac{I^2 r}{2} \)
- \( P_3 = \frac{I^2 r}{2} \)
Therefore, the order of power dissipated is:
**P2 > P1 > P4 = P3**, which corresponds to Option A.
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