Physics - Error Question with Solution | TestHub

Given:

Voltmeter resistance: $R_v=500ohms$

Internal resistance of the cell: $r=4ohms$

EMF of the cell: $E$

Step 1: Total resistance when voltmeter is connected

$R_{total}=R_v+r=500+4=504ohms$

Step 2: Current in the circuit

$I=\frac{E}{R_{t}otal}=\frac{E}{504}$

Step 3: Measured voltage by voltmeter

$V=I\cdot R_v=\frac{E}{504}\cdot 500=\frac{500E}{504}$

Step 4: Percentage error

Percentage Error = $\frac{Actualvalue-Measuredvalue}{Actualvalue}\cdot 100$

Percentage Error = $\frac{E-V}{E}\cdot 100$

Percentage Error = $\frac{E-\frac{500E}{504}}{E}\cdot 100$

Percentage Error = $\left(1-\frac{500}{504}\right)\cdot 100$

Percentage Error = $\frac{4}{504}\cdot 100\approx 0.79365\%$

Step 5: Rounded value

Percentage Error $\approx 0.8\%$

Answer:

The percentage error in the reading of the voltmeter is approximately 0.8 %.