A 6-ohm resistance wire is doubled by folding. What is the new resistance?

Answer:

The electrical resistance of a circuit is the ratio between the voltage applied to the current flowing through it.

According to Ohm’s law, there is a relation between the current flowing through a conductor and the potential difference across it. It is given by,

 I V = IR

Where,
  • V = Potential difference measured across the conductor (in volts)
  • I = Current through the conductor (in amperes)
  • R = Constant of proportionality called resistance (in ohms)

Given

R = 6 Ohms

\(\begin{array}{l}R = \frac{\rho l}{A}\end{array} \)
————-(1)

Wire is doubled so,

  • Area (A) = 2A
  • length (l) = l/2

New Resistance will be:

\(\begin{array}{l}R_{new} = \frac{\rho (\frac{l}{2})}{2A}\end{array} \)

 

Rnew = ρl/4A

By using eqaution (1) we can simplify the above equation as

Rnew = R/4

Rnew = 6/4

Rnew = 1.5 Ohms

Hence, the new Resistance of wire is 1.5 Ohms.

For additional information on resistance and Ohm’s Law, refer to the video

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