A wire of resistance 2R is stretched such that its length is doubled. Then the increase in its resistance is:
A wire of resistance 2R is stretched such that its length is doubled. Then the increase in its resistance is:
6R
4R
3R
2R
The Correct Option is A
Solution and Explanation
The correct option is: (A) : 6R
R = ρ * (L / A)
Where:
- R is resistance
- ρ is resistivity of the material
- L is the length of the wire
- A is the cross-sectional area of the wire
Since the wire's length is doubled, the new length becomes 2L. However, its cross-sectional area doesn't change due to stretching. So the new resistance (R_new) can be expressed as:
R_new = ρ * (2L / A)
The increase in resistance (ΔR) is the difference between the new resistance and the initial resistance:
ΔR = R_new - R ΔR = ρ * (2L / A) - ρ * (L / A) ΔR = ρ * (2L - L) / A ΔR = ρ * L / A
Now, since the initial resistance was 2R, we can equate ΔR to 6R:
ρ * L / A = 6R
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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.