A current of 5A is passing through a metallic wire of cross-sectional area $4\times10^{-6}m^2$ If the density of the charge carriers in the wire is 5 ? $10^{26}m^{-3}$, the drift speed of the electrons will be [e = 1.602 ? $10^{-19}C$]
- $1.56 \times 10^{-2}ms^{-1}$
- $1.98 ?10^{-2}ms^{-1}$
- $2.42 ?10^{-2}ms^{-1}$
- $2.84 ?10^{-2}ms^{-1}$
The Correct Option is A
Solution and Explanation
Another way is to simplify using step-by-step cancellation of powers of ten first.
Given:
\(v_d = \frac{I}{n A e}\)
Substitute values:
\(v_d = \frac{5}{(5 \times 4 \times 1.602) \times (10^{26} \times 10^{-6} \times 10^{-19})}\)
Now combine exponents:
\(10^{26-6-19} = 10^{1}\)
So:
\(v_d = \frac{5}{5 \times 4 \times 1.602 \times 10}\)
Cancel 5:
\(v_d = \frac{1}{4 \times 1.602 \times 10}\)
\(v_d = \frac{1}{64.08}\)
\(v_d \approx 1.56 \times 10^{-2}\,\text{m/s}\)
Final answer: \(1.56 \times 10^{-2}\,\text{m/s}\)
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Concepts Used:
Current Electricity
Current electricity is defined as the flow of electrons from one section of the circuit to another.
Types of Current Electricity
There are two types of current electricity as follows:
Direct Current
The current electricity whose direction remains the same is known as direct current. Direct current is defined by the constant flow of electrons from a region of high electron density to a region of low electron density. DC is used in many household appliances and applications that involve a battery.
Alternating Current
The current electricity that is bidirectional and keeps changing the direction of the charge flow is known as alternating current. The bi-directionality is caused by a sinusoidally varying current and voltage that reverses directions, creating a periodic back-and-forth motion for the current. The electrical outlets at our homes and industries are supplied with alternating current.