Question

a potential difference of v=(20+_1)volt is applied across the resistance of(8+_2)ohm.calculate the current with error limit​

Answer 1

I=(2.5+_0.75)A is the current with error limit

Answer 2

Given :

Potential Difference (V) = (20 ± 1) V

Resistance (R) = (8 ± 2) ohm

To Find :

Current with error limit

Solution :

As per Ohm's Law,

                   Potential Difference (V) = Current (i) × Resistance (R)

⇒                         Current (i)               = $\frac{V}{R}$

⇒                          Current (i)              = $\frac{20}{8}$

∴                           Current (i)              = 2.5 A

Now for calculating the error, we have

             Δi/i           =  ΔV/V   +  ΔR/R

⇒           Δi             =  (ΔV/V   +  ΔR/R) × i

⇒           Δi             = $(\frac{1}{20} + \frac{2}{8} )$ × 2.5

⇒           Δi             = $\frac{2 + 10}{40}$ × 2.5

⇒           Δi             = $\frac{12}{40}$ × 2.5

∴            Δi             = 0.75 A

Therefore, Current is (2.5 ± 0.75) A