What will happen when a 40 watt-220 volt lamp and a 100 watt-220 volt lamp are connected in series across 40 volt supply?

# What will happen when a 40 watt-220 volt lamp and a 100 watt-220 volt lamp are connected in series across 40 volt supply?

1. A

100 watt lamp will fuse

2. B

40 watt lamp will fuse

3. C

Both lamps will fuse

4. D

Neither lamp will fuse

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### Solution:

Bulb (I): Rated current ${\mathrm{I}}_{1}\text{\hspace{0.17em}}=\frac{\mathrm{P}}{\mathrm{V}}\text{\hspace{0.17em}}=\text{\hspace{0.17em}\hspace{0.17em}}\frac{40}{220}\text{\hspace{0.17em}}=\frac{2}{11}\text{\hspace{0.17em}}\mathrm{A}$

Resistance, ${\mathrm{R}}_{1}=\frac{{\mathrm{V}}^{2}}{\mathrm{P}}\text{\hspace{0.17em}\hspace{0.17em}}=\text{\hspace{0.17em}}\frac{{\left(220\right)}^{2}}{40}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}1210\text{\hspace{0.17em}}\mathrm{\Omega }$

Bulb (II) : Rated current, ${\mathrm{I}}_{2}\text{\hspace{0.17em}\hspace{0.17em}}=\text{\hspace{0.17em}\hspace{0.17em}}\frac{100}{220}=\text{\hspace{0.17em}}\frac{5}{11}\text{\hspace{0.17em}\hspace{0.17em}}\mathrm{A}$

Resistance, ${\mathrm{R}}_{2}=\text{\hspace{0.17em}}\frac{{\left(220\right)}^{2}}{100}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}484\text{\hspace{0.17em}}\mathrm{\Omega }$

When both are connected in series across 40 V supply

Total current through supply

${\mathrm{R}}_{1}=\text{\hspace{0.17em}}\frac{40}{{\mathrm{R}}_{1}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}{\mathrm{R}}_{2}}\text{\hspace{0.17em}}=\frac{40}{1210+484}=\frac{40}{1694}=0.023\text{\hspace{0.17em}}\mathrm{A}$

This current is less than the rated current of each bulb. So neither bulb will fuse.

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