1.

A wire is cut into three equal parts and then connected in parallel with the same source. How will its.(i) resistance and resistivity gets affected? (ii) How would the total current and the current through the parts change?

Answer»

i. Here, the new resistance: R = \(\frac{R}{3}\)

\(\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}\)

\(\frac{1}{R_{eq}}=\frac{1}{\frac{R}3}+\frac{1}{\frac{R}3}+\frac{1}{\frac{R}{3}}\)

\(\frac{1}{R_{eq}}=\frac{3}{R}+\frac{3}{R}+\frac{3}{R}\)

\(\frac{1}{R_{eq}}=\frac9R\)

\(\frac{1}{R_{eq}}=\frac9RΩ\)

The resistivity is dependent on the nature of the material. 

Hence, there will be no change in the reisitivity of the wire. 

ii. Now, by Ohm’s Law

V = I x R

I = \(\frac{V}R=\frac{V}{\frac{R}9}=\frac{9V}{R}\)

∴ I = 9 x I

Thus, the current will increase 9 times than the previous current.


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