A wire has resistance of 20 ohm it's length is now stretched to increa...
Explanation:
To calculate the new resistance of the wire after it is stretched, we need to consider the effect of the change in length on the wire's resistance. The resistance of a wire is directly proportional to its length. This means that when the length of the wire increases, the resistance also increases.
The resistance of a wire can be calculated using the formula:
R = ρ * (L/A)
Where:
R is the resistance of the wire
ρ is the resistivity of the material of the wire
L is the length of the wire
A is the cross-sectional area of the wire
In this case, the resistivity and the cross-sectional area of the wire remain constant. So, we can focus on the change in length of the wire.
Step 1: Calculate the new length of the wire:
Since the wire is stretched by 2%, the new length of the wire can be calculated by adding 2% of the original length to the original length.
Let's assume the original length of the wire is 'L'. The new length of the wire, 'L_new', can be calculated as:
L_new = L + 0.02 * L
Step 2: Calculate the new resistance:
Now, we can substitute the new length into the resistance formula to calculate the new resistance of the wire.
R_new = ρ * (L_new/A)
Since the resistivity and the cross-sectional area remain constant, we can simplify the equation as:
R_new = R * (L_new/L)
Substituting the value of L_new from Step 1, we get:
R_new = R * ((L + 0.02 * L)/L)
Simplifying further:
R_new = R * (1 + 0.02)
R_new = R * 1.02
Therefore, the new resistance of the wire is 1.02 times the original resistance. In this case, the new resistance would be:
New resistance = 20 ohm * 1.02 = 20.4 ohm
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