Question

2. A current of 3.5 ± 0.5 A flows through metallic conductor with a potential difference of 21 ± 1 V is applied. Find the resistance of the wire.

Answer 1

according to Ohm's law , V = IR

where V is potential difference , R is resistance and I is current through the wire.

To find resistance use formula, R = V/I

given, I = (3.5 ± 0.5)A

and V = (21 ± 1) v

value of R without including error , R = V/I = 21/3.5 = 6 ohm.

now, To find error, use formula

∆R/R = ∆V/V + ∆I/I

here , R = 6, ∆V = 1, V = 21 , ∆I = 0.5 and I = 3.5

so, ∆R/6 = 1/21 + 0.5/3.5

or, ∆R = 6(1/21 + 1/7) = 6 × 4/21

= 24/21 = 8/7 ≈ 1.1428

hence, resistance = (6 ± 1.1428) Ohm.

Answer 2

Answer:

Resistance = (6 ± 1.1428) Ohm.

Explanation:

Given Problem:

A current of 3.5 ± 0.5 A flows through metallic conductor with a potential difference of 21 ± 1 V is applied. Find the resistance of the wire.

Solution:

According to Ohm's law,

R = $\frac{V}{I}$

V is potential difference

R is resistance.

I is current through the wire.

To find resistance we have to use this formula,

R = $\frac{V}{I}$

Given that,

I = (3.5 ± 0.5)A  

V = (21 ± 1) v

Value of R without including error , $R = \frac{V}{I} = \frac{21}{3.5} = 6\ ohm$

Now,

To find error we know that,

$\triangle \frac{R}{R} = \triangle\frac{V}{V}+ \triangle\frac{I}{I}$

R = 6, ∆V = 1, V = 21 , ∆I = 0.5 and I = 3.5

So,

∆R/6 = 1/21 + 0.5/3.5  

∆R = 6(1/21 + 1/7) = 6 × 4/21  

= 24/21 = 8/7 ≈ 1.1428  

Hence,

Resistance = (6 ± 1.1428) Ohm.