Correct Answer - Option 3 : 1.00 Ω
CONCEPT:
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Resistance (R): The resistance offered to the flow of current is known as the resistance.
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SI unit of resistance is the ohm (Ω).
- Mathematically resistance can be written as
\(⇒ R = \frac{{\rho l}}{A}\)
Where R = resistance, l = length, A = area of cross-section and ρ = resistivity
EXPLANATION:
- That wire is doubled on it means to fold the length of wire. That is its length will get half and the area of the cross-section will get doubled.
Given: R1 = R = 4 Ω
As we know that the resistance of the wire is,
\(\Rightarrow R = \frac{{\rho l}}{A}\)
When the wire is doubled then, then its area will increase automatically. But the volume of the wire will be the same.
∴ The volume of original wire = volume of new wire
⇒ A1l1 = A2l2
⇒ A1l1 = A2 l1/2
⇒ A2 = 2A1
- The resistance of the wire in 1st case
\(\Rightarrow {R_1} = R = \frac{{\rho {l_1}}}{{{A_1}}}\) ----(1)
- The resistance of the wire in 2nd case
\(\Rightarrow {R_2} = \frac{{\rho {l_2}}}{{{A_2}}} = \frac{{\rho {\frac{l_1}{2}}}}{{{2A_1}}} = \frac{{\rho {l_1}}}{{{4A_1}}}\) -----(2)
Divide equation 1 and 2, we get
\(\Rightarrow \frac{R}{{{R_2}}} = \frac{{\frac{{\rho {l_1}}}{{{A_1}}}}}{ \frac{{\rho {l_1}}}{{{4A_1}}}} = 4\)
⇒ R2 = 1 Ω