Two electric bulbs rated P1 watt V volts and P2 watt V volts are connected in parallel and V volts are applied to it. The total Power will be

# Two electric bulbs rated P1 watt V volts and P2 watt V volts are connected in parallel and V volts are applied to it. The total Power will be

1. A

$\left({\mathrm{P}}_{1}+{\mathrm{P}}_{2}\right)\text{\hspace{0.17em}}\mathrm{watt}$

2. B

$\sqrt{{\mathrm{P}}_{1}+{\mathrm{P}}_{2}}\text{\hspace{0.17em}}\mathrm{watt}$

3. C

$\frac{{\mathrm{P}}_{1}{\mathrm{P}}_{2}}{{\mathrm{P}}_{1}+{\mathrm{P}}_{2}}\text{\hspace{0.17em}}\mathrm{watt}$

4. D

$\frac{{\mathrm{P}}_{1}+{\mathrm{P}}_{2}}{{\mathrm{P}}_{1}{\mathrm{P}}_{2}}\text{\hspace{0.17em}}\mathrm{watt}$

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### Solution:

If resistances of bulbs are R1 and R2, respectively, then in parallel $\frac{1}{{\mathrm{R}}_{\mathrm{P}}}\text{\hspace{0.17em}}=\text{\hspace{0.17em}\hspace{0.17em}}\frac{1}{{\mathrm{R}}_{1}}+\frac{1}{{\mathrm{R}}_{2}}$

$⇒\text{\hspace{0.17em}\hspace{0.17em}}\frac{1}{\left(\frac{{\mathrm{V}}^{2}}{{\mathrm{P}}_{\mathrm{p}}}\right)}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\frac{1}{\left(\frac{{\mathrm{V}}^{2}}{{\mathrm{P}}_{1}}\right)}+\frac{1}{\left(\frac{{\mathrm{V}}^{2}}{{\mathrm{P}}_{2}}\right)}\text{\hspace{0.17em}}⇒\text{\hspace{0.17em}\hspace{0.17em}}{\mathrm{P}}_{\mathrm{P}}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}{\mathrm{P}}_{1}+{\mathrm{P}}_{2}$

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