A wire of resistance $0.1 o h m c m^{- 1}$ bent to form a square ABCD of side $10 c m$ . A similar wire is connected between the corners $B$ and $D$ to form the diagonal $B D$ . Find the effective resistance of this combination between corners $A$ and $C$ . If a $2 V$ battery of negligible internal resistance is connected across $A$ and $C$ . Calculate the total power dissipated.

1 Ω, 3 W

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1 Ω, 4 W

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2 Ω, 4 W

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2 Ω, 3 W

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Solution

The correct option is B $1 Ω, 4 W$
Resistance of sides of equale $= 0.1 \times 10 = 1 Ω$
$△ a$ circle is
here which $△$ base bridge is formed
$\frac{R_{1}}{R_{2}} = \frac{R_{1}}{R_{4}}$
so current between $B D$ is zero
then Reff of where cict
Reff $= \frac{1 Ω}{1 Ω}$
$\equiv R e f f$
Power $= \frac{V^{2}}{R e f f}$
$= \frac{(2)^{2}}{1}$
$= 4 W$

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The correct option is B 1Ω ,4 WResistance of sides of equale =0.1×10=1 Ω△a circle ishere which △ base bridge is formed R1R2=R1R4so current between BD is zerothen Reff of where cictReff =1 Ω1 Ω≡ReffPower =V2Reff=(2)21=4 W