If a copper wire is stretched to increase its length by \(20 \%\) The percentage increase in resistance of the wire is _______\(\%\).
If a copper wire is stretched to increase its length by \(20 \%\) The percentage increase in resistance of the wire is _______\(\%\).
Show Hint
When a wire is stretched, the resistance increases as R ∝ L2 (if volume remains constant).
Correct Answer: 44
Approach Solution - 1
Solution:
The resistance of a wire is given by:
\[ R = \rho \frac{L}{A} \]
where \(L\) is the length and \(A\) is the cross-sectional area. When a wire is stretched, its volume remains constant:
\[ L_1 A_1 = L_2 A_2 \]
As \(L_2 = 1.2L_1\), the area decreases as:
\[ A_2 = \frac{A_1}{1.2} \]
The new resistance is:
\[ R_2 = \rho \frac{L_2}{A_2} = \rho \frac{1.2L_1}{A_1 / 1.2} = 1.44R_1 \]
The percentage increase in resistance is:
\[ \% \, \text{Increase} = \frac{R_2 - R_1}{R_1} \times 100 = \frac{1.44R_1 - R_1}{R_1} \times 100 = 44\% \]
Thus, the resistance increases by 44%.
Approach Solution -2
The correct answer is 44.
As volume is constant,
So resistance ∝ (length )2
⇒% change in resistance
\(\frac{1.44 R_0}{R_0}×100=0.44×100\)
\(=44\%\)
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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.