Question

Four identical electrical lamps are labelled $1.5 \,V$, $0.5\, A$ which describes the condition necessary for them to operate at normal brightness. If a $12\, V$ battery of negligible internal resistance is connected to lamps as shown, then

• A. the value of $R$ for normal brightness of each lamp is $(3 / 4) \Omega$
• B. the value of $R$ for normal brightness of each lamp is $(21 / 4) \Omega$
• C. total power dissipated in circuit when all lamps are normally bright is $24\, W$
• D. power dissipated in $R$ is $21 W$ when all lamps are normally bright

Answer 1

Answer: (B)

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 $
$\Rightarrow 10.5=2 \times R$
$=R=\frac{21}{4} \Omega$