Question

1. a Wire haing a resistance of 18 ohms is cut into 3 equal parts. What is the equivalent resistance if these three parts are joined in parallel?

Answer 1

Resistance of each part = 18/3 = 6 ohm

So, if they are connected in parallel, the equivalent resistance will be
1/Rp = 1/R1 + 1/R2 + 1/R3
1/Rp = 1/6 + 1/6 + 1/6
1/Rp = 3/6
1/Rp = 1/2
Rp = 2 ohm

So, the equivalent resistance is 2 ohm.

Answer 2

Answer:

2 Ω is the required value of equivalent resistance .

Explanation:

Given , resistance of a wire = 18 Ω

And the wire is cut into 3 equal parts .

So, each wire has resistance = $\frac{18}{3}$ = 6 Ω

Let , the three equal resistance be $R_1 , R_2 and \ R_3$ .

According to the question resistance are joined in parallel ,

⇒$\frac{1}{R} = \frac{1}{R_1} +\frac{1}{R_2} +\frac{1}{R_3}$

Where , $R_1 = R_2 = R_3$ = 6 Ω .

Therefore ,

$\frac{1}{R} = \frac{1}{6} + \frac{1}{6} +\frac{1}{6}$

⇒$\frac{1}{R} = \frac{1+1+1}{6}$ = $\frac{3}{6} = \frac{1}{2}$ Ω

⇒R = 2 Ω

Hence , 2 Ω is the equivalent resistance .

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