Question

Find the uncertainty in a calculated electrical potential difference from the measurements of current and resistance. Electric potential difference depends on current and resistance according to this function V(I,R) = IR. Your measured current and resistance have the following values and uncertainties I = 5.9 Amps, delta I space equals space 0.4 Amps and R = 42.7 Ohms and delta R space equals space 0.6 Ohms. What is the uncertainty in the , delta V ? Units are not needed in your answer.

Answer 1

ΔV = 2 10¹ V

Step-by-step explanation:

The calculation of the uncertainty or error in an expression is given by

ΔV =
`(dV)/(di)` |Δi| +
`(dV)/(dR)` |ΔR |

V = i R

let's make the derivatives

`(dV)/(di)` = R

`(dV)/(dR)` = i

we substitute

ΔV = R | Δi | + i | ΔR |

in the exercise give the values

i = (5.9 ± 0.4) A

R = (42.7 ± 0.6) Ω

we calculate

ΔV = 42.7 0.4 + 5.9 0.6

ΔV = 20.6 V

ΔV = 2 10¹ V

the voltage is

V = i R

V = 5.9 42.7

V = 251.9 V

the result is

V = (25 ± 2) 10¹ V