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Directions : In the following question more than one of the answers given may be correct. Select the correct answer and mark it according to the code:

Four identical electrical lamps are labelled 1.5 V, 0.5 A which describes the condition necessary for them to operate at normal brightness. A 12V battery of negligible internal resistance is connected to lamps as shown then (1) the value of R for normal brightness of each lamp is\[(3/4)\Omega \] (2) the value of R for normal brightness of each lamp is \[(21/4)\Omega \] (3) total power dissipated in circuit when all lamps are normally bright is 24 W. (4) power dissipated in R is 21 W when all lamps are normally bright

A)  1, 2 and 3 are correct

B)  1 and 2 are correct

C)   2 and 4 are correct

D)  1 and 3 are correct

Correct Answer: C

Solution :

                 For normal brightness of each bulb see following circuit. Current through each bulub\[=0.5A\]                                 So, main current\[i=2\text{ }A\]                 Also, voltage across the combination\[=1.5\text{ }V\]                 So, voltage across the resistance \[=10.5\text{ }V\]                 Hence, for resistance\[V=iR\]                 \[\Rightarrow \]               \[10.5=2\times R\]                          \[\Rightarrow \]               \[R=\frac{21}{4}\Omega \]                 Power dissipated in\[R=\frac{{{(10.5)}^{2}}}{21/4}=21\,W\].