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

Line 2021-02-13 Answered
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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BleabyinfibiaG
Answered 2021-02-14 Author has 3904 answers
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, \(\displaystyle{R}_{{{2}}}={30.72}={4}{R}_{{{1}}}\)
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