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

# 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

1. A

the value of R for normal brightness of each lamp is $\left(3/4\right)\text{\hspace{0.17em}\hspace{0.17em}}\Omega$

2. B

the value of R for normal brightness of each lamp is $\left(21/4\right)\text{\hspace{0.17em}\hspace{0.17em}}\Omega$

3. C

total power dissipated in circuit when all lamps are normally bright is 24 W

4. D

power dissipated in R is 2l W when all lamps ate normally bright

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### Solution:

For normal brightness of each bulb see following circuit. Current through each bulb = 0.5 A

So main current  i = 2A
Also, voltage across the combination = 1.5 V
So voltage across the resistance = 10.5 V
Hence. for resistance, $\mathrm{V}=\mathrm{iR}\text{\hspace{0.17em}}⇒\text{\hspace{0.17em}\hspace{0.17em}}10.5=2\text{\hspace{0.17em}\hspace{0.17em}}×\text{\hspace{0.17em}\hspace{0.17em}}\mathrm{R}=\mathrm{R}\text{\hspace{0.17em}}=\frac{21}{4}\text{\hspace{0.17em}}\mathrm{\Omega }$

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