# The formula V= sqrt{PR} relates the voltage V (in volts), power P (in watts), and resistance R (in ohms) of an electrical circuit. The hair dryer show

The formula $$\displaystyle{V}=\sqrt{{{P}{R}}}$$ relates the voltage V (in volts), power P (in watts), and resistance R (in ohms) of an electrical circuit. The hair dryer shown is on a 120-volt circuit. Is the resistance of the hair dryer half as much as the resistance of the same hair dryer on a 240-volt circuit? Explain your reasoning.

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Given information: $$\displaystyle{V}=\sqrt{{{P}{R}}},\ {V}_{{{1}}}={120}\ \text{and}\ {P}={1875}$$
$$\displaystyle{V}_{{{2}}}={240}$$ Formula Used: Simplify. Calculation: $$\displaystyle{V}=\sqrt{{{P}{R}}}$$
$$\displaystyle\text{AS}\ {V}_{{{1}}}={120}\ \text{and}\ {P}={1875}$$ So, $$\displaystyle{120}=\sqrt{{{1875}\ \times\ {R}_{{{1}}}}}$$ Now, squaring both sides $$\displaystyle{14400}={1875}\ \times\ {R}_{{{1}}}$$ So, $$\displaystyle{R}_{{{1}}}={\frac{{{14400}}}{{{1875}}}}$$ Hence, $$\displaystyle{R}_{{{1}}}={7.68}$$ As $$\displaystyle{V}_{{{2}}}={240}\ \text{and}\ {P}={1875}$$ So, $$\displaystyle{240}=\ \sqrt{{{1875}\ \times\ {R}_{{{2}}}}}$$ Now, squaring both sides $$\displaystyle{57600}={1875}\ \times\ {R}_{{{2}}}$$ So, $$\displaystyle{R}_{{{2}}}=\ {\frac{{{57600}}}{{{1875}}}}$$ Hence, $$\displaystyle{R}_{{{2}}}={30.72}={4}{R}_{{{1}}}$$