Question

Four identical electrical lamps are labelled $1.5V$, $0.5A$ which describes the condition necessary for them to operate at normal brightness. If a $12V$ 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 $24W$
• D. power dissipated in $R$ is $21W$ when all lamps are normally bright

Answer 1

Answer: (B)

For normal brightness of each bulb see following circuit. Current through each bulb $=0.5A$
So main current $i=2A$

Also, voltage across the combination $=1.5V$
So voltage across the resistance $=10.5V$
Hence, for resistance, $V=iR$
$\Rightarrow 10.5=2\times R$
$=R=\frac{21}{4}\Omega$