Question

Four identical electrical lamps are labelled $1.5V,0.5A,$ which describes the condition necessary for them to operate at normal brightness. $A12V$ battery of negligible internal resistance is connected to lamps as shown then

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

Answer 1

The correct option is B The value of $R$ for normal brightness of each lamp is $\left(21/4\right)\Omega$

Figure shown below is for normal brightness of each bulb
Given, Current through each bulb
$i_0=0.5A$
For $4$ electric bulbs, current through mains supply
$\Rightarrow i_0=\left(0.5\right)4=2A$
Also, voltage drop across each bulb
$V_0=1.5V$
Then, voltage drop across resistaance
$V_R=E-V_0=12-1.5=10.5V$
Where $E=12V$ is emf of battery
Hence for resistance $R,$ we know that
$V_R=iR$
$\Rightarrow 10.5=i\times R=2\times R$
$R=\frac{21}{4}\Omega$

Hence, option $\left(b\right)$ is correct.