If a 4 ohms resistance wire is doubled, determine its new resistance.

Resistance can be depicted as the ratio between the applied voltage to the current flowing through a circuit. The S.I. unit of resistance is Ohms (Ω).

Determine the Given Data

Initial resistance on the wire, R_i = 4 Ω

Assuming that the initial length of the wire = L_i.

As per the given equation, the final length of the wire L_f =2L_i

Consider area of the wire = A.

Consider the resistivity of the wire = ρ.

Consider final resistance of the wire = R_f.

Formula Used

We know that resistance is given as,

⇒ \(R = \rho{{L} \over A}\)

⇒ \(\rho= {{RA} \over L}\)

Calculation of New Resistance

Since the resistivity of the wire remains the same in both, we can mention:

\(\rho = {{R_i A} \over L_i} = {{R_fA} \over L_f}\)

⇒ \({{R_i} \over L_i} = {{R_f} \over L_f}\)

Upon value substitution, we can get,

\({{4} \over Li} = {{R_f} \over 2L_i}\)

⇒ R_f= 8 \(\Omega\)

Therefore, the new resistance is 8\(\Omega\).

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If a 4 ohms resistance wire is doubled, determine its new resistance.

Determine the Given Data

Formula Used

Calculation of New Resistance

Related Questions

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If a 4 ohms resistance wire is doubled, determine its new resistance.

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Calculation of New Resistance

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5.What is displacement current (\( i_d \))? Considering the case of charging of a capacitor, show that \( i_d = \varepsilon_0 \frac{d\Phi_E}{dt} \). What is the value of \( i_d \) for a conductor across which a constant voltage is applied?

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