Question

For a device, power consumed = 110 W and voltage supplied is 220 V. The number of electrons that flow in 1 is \(\frac{x}{4}\) × 10¹⁷ . Find x.

Answer 1

Correct Answer: 125

To find \( x \) we need to determine the number of electrons that flow in 1 second given the power consumed and the voltage supplied. Power \( P \) is given by the formula:

P = V \cdot I

where \( P = 110 \) W and \( V = 220 \) V. We can solve for the current \( I \):

I = \frac{P}{V} = \frac{110}{220} = 0.5 A

The current \( I \) is the charge flow per unit time in coulombs per second, and 1 A = 1 C/s. The charge of one electron is \( e = 1.6 \times 10^{-19} \) C. The number of electrons \( n \) flowing per second is given by:

n = \frac{I}{e} = \frac{0.5}{1.6 \times 10^{-19}}

Calculating \( n \):

n = 3.125 \times 10^{18}

The number of electrons flowing expressed as \(\frac{x}{4}\) × 10¹⁷ implies:

\(\frac{x}{4}\) \times 10^{17} = 3.125 \times 10^{18}

Simplify to find \( x \):

\frac{x}{4} = 31.25

Multiply by 4:

x = 31.25 \times 4 = 125

Thus, the value of \( x \) is 125, which falls within the expected range [125,125].