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 $12\,V$ battery of negligible internal resistance is connected to lamps as shown, then
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For normal brightness of each bulb see following circuit. Current through each bulb $=$ $0.5\, A$
So main current $i = 2\,A$
Also, voltage across the combination $ = 1.5\,V$
So voltage across the resistance $ = 10.5\,V$
Hence for resistance $V = i\,R$ $ \Rightarrow $ $10.5 = 2 \times R$ $ \Rightarrow $ $R = \frac{{21}}{4}\,\Omega $
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