Figure shows three resistor configurations $R_{1}$ , $R_{2}$ and $R_{3}$ connected to a 3 V battery. If the power dissipated by the configuration $R_{1}$ , $R_{2}$ and $R_{3}$ is $P_{1}$ , $P_{2}$ and $P_{3}$ , respectively, then [2008]

Question

Smart Achievers · Accepted Answer

(3)

We know power, $P = \frac{V^{2}}{R}$

And V is constant in all three cases. $∴$ $P \propto \frac{1}{R}$

Case (i)

This is a case of balanced Wheatstone bridge $R_{1} = 1 Ω$

Case (ii)

$\frac{1}{R_{2}} = \frac{1}{2} + \frac{1}{1} + \frac{1}{2}$ $\Rightarrow R_{2} = \frac{2}{4}$ $= \frac{1}{2} 52$

Case (iii)

Thus $R_{3} = 2 Ω$

$Since, R_{2} < R_{1} < R_{3}$ $∴$ $P_{2} > P_{1} > P_{3}$

Solution

Q.
Figure shows three resistor configurations $R_{1}$ , $R_{2}$ and $R_{3}$ connected to a 3 V battery. If the power dissipated by the configuration $R_{1}$ , $R_{2}$ and $R_{3}$ is $P_{1}$ , $P_{2}$ and $P_{3}$ , respectively, then [2008]

1 $P_{1} > P_{2} > P_{3}$

2 $P_{1} > P_{3} > P_{2}$

3 $P_{2} > P_{1} > P_{3}$

4 $P_{3} > P_{2} > P_{1}$

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Solution

Q. Figure shows three resistor configurations R1, R2 and R3 connected to a 3 V battery. If the power dissipated by the configuration R1, R2 and R3 is P1, P2 and P3, respectively, then [2008]

1 P1>P2>P3

2 P1>P3>P2

3 P2>P1>P3

4 P3>P2>P1