Question

What is the minimum number of bulbs, each marked $60W,40V,$ that can work safely when connected in series with a $240V$ mains supply?

• A. $2$
• B. $4$
• C. $6$
• D. $8$

Answer 1

The correct option is C $6$

Resistance of each bulb

$R=\frac{V^2}{P}$

$\Rightarrow R=\frac{(40{)}^2}{60}$

$\Rightarrow R=26.67\Omega$

Maximum current that can flow through the bulb without damaging it

$I_{max}=\frac{P}{V}$

$\Rightarrow I_{max}=\frac{60}{40}$

$\Rightarrow I_{max}=1.5A$

Thus minimum resistance required in the circuit

$R_{min}=\frac{V_s}{I_{max}}$

$\Rightarrow R_{min}=\frac{240}{1.5}$

$\Rightarrow R_{min}=160\Omega$

Let $n$ number of bulbs are connected in series in the circuit.

Equivalent resistance of $n$ bulbs

$R_{eq}=nR=26.67n$

But,

$26.67n\le 160$

$\Rightarrow n\le 6$

Thus minimum number of bulbs required is $6$.