Question

The resistance of a 1m long nichrome wire is 6 W. If we reduce the length of the wire to 70 cm. what will its resistance be?(Answer : 4.2 Ω). Solve the problem

Answer 1

In first case :-
Length = 1 m.
Resistance = 6 Ω.
Area if cross section = a

Now, Resistivity = $\frac{Ra}{l}$
$\rho = \frac{6 * a }{1}$
$\rho = 6a$ ----→ (I)


In second case :-
Length = 70 cm = 0.7 m
Resistance = R
Area of cross section = a

Now, Resistivity =$\frac{Ra}{l}$
$\rho = \frac{Ra}{0.7}$ -----(ii)

Since for the same material the resitivity will be same whether the area or the length either decrease or increase, therefore . from eq I and ii

$6a = Ra/0.7$
R = 6 × 0.7
R = 4.2 Ω.

Hence the resistance is 4.2 ohm.

Hope it Helps .

Answer 2

Answer:

so according to the first  law of resistance

R1/R2=L1/L2   here R1 is resistance of first wire,R2 is resistance of new wire and L1 is length of first wire,L2 is length of second wire

so 6Ω/R2=100/70

which implies R2=4.2Ω

hope it helps you Have a great day!!!!!!!iiiiiiii

Explanation: