Question

Electric bulb $50W-100V$ glowing at full power are to be used in parallel with battery $120V,10\Omega$. Maximum number of bulbs that can be connected so that they glow in full power is

• A. $4$
• B. $6$
• C. $8$
• D. $2$

Answer 1

The correct option is A $4$

Step 1: Calculation of current

Power rating of each bulb $=50W$

Voltage $=100V$


So, the current flowing through each bulb when they are glowing at full power is

$I=\frac{P}{V}=\frac{50}{100}=\frac{1}{2}A$

Step 2: Calculation of number of bulbs

Current flowing through main supply,

$i=\frac{1}{2}\times n$

Where $n$ is the number of bulbs

Also for the battery of emf $E$ and internal resistance $r$

$E=V+ir$

Where,

$V$ is the voltage drop across the bulb $=100V$

Also it is given,

$E=120V,r=10\Omega$

$\therefore 120=100+(\frac{n}{2}\times 10)$

$\Rightarrow 20=5n$

$\Rightarrow n=4$

Hence, option (c) is correct.