Question

A particular resistance wire has a resistance 3.0 ohm per metre.
Find :

The total resistance of three lengths of this wire each 1.5 m long, joined in parallel.​

Answer 1

Resistance of 1 metre is 3 ohm.

So,

Resistance of 1.5 metre = 1.5 * 3 = 4.5 ohm

So,

there are three Resistance of 4.5 ohm connected in parallel.

Formula of Equivalent Resistance for Parallel connection for same type of Resistance

= Resistance / Number of Resistance

Applying formula,

4.5 ohm / 3 = 1.5 ohm

Answer

So, total resistance will be 1.5 ohm

Thank you.

Answer 2

$\LARGE{ \underline{ \bf{Required \: answer:}}}$

• $\large{ \boxed{ \boxed{ \rm{1.5 \: ohm}}}}$

Explanation:

We have,

Resistance of 1 m wire = 3 Ω

Now, we know that resistance is directly proportional to length and is given by R = Resistivity × Length / Cross-sectional Area. Resistivity and Cross sectional area will remain same, then Resistance will vary with length.

Then,

Resistance of 1.5 m wire = 3 × 1.5 Ω = 4.5 Ω

So, we have three lengths of resistors with resistance 4.5 Ω. They are connected in parallel. Then equivalent resistance:

$\rm{ \dfrac{1}{R_eq.} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \dfrac{1}{R_3}}$

We have, R1 = R2 = R3. Hence Req. = R/3

$\rm{R_eq. = \dfrac{4.5}{3} } = 1.5 ohm$

And we are done! :D