Physics

Problem

A cell of emf

E

and internal resistance

r

is connected to an external resistor

R

. A voltmeter of resistance

R_{v}

is used to measure the potential difference across

R

. a. (a) Derive an expression for the potential difference across

R

when no voltmeter is connected. b. (b) Show that this potential difference equals

E \times \dfrac{R}{R+r}

. c. (c) When the voltmeter is connected across

R

, derive an expression for the reading on the voltmeter. d. (d) Using

E = 1.5\,\text{V}

r = 1\,\Omega

R = 9\,\Omega

and

R_{v} = 45\,\Omega

, calculate (i) the true potential difference across

R

and (ii) the voltmeter reading. Hence determine the percentage error introduced by the voltmeter.