Physics - Error Question with Solution | TestHub

Given:

Ammeter resistance: $R_A=1ohm$

External resistance: $R=48ohms$

EMF: $E=10V$

Internal resistance of source: $r=1ohm$

Step 1: Total resistance (ammeter included)

$R_{total}=R+r+R_A=48+1+1=50ohms$

Step 2: Current with ammeter resistance

$I_{actual}=\frac{E}{R_{total}}=\frac{10}{50}=0.2A$

Step 3: Current if ammeter is ideal (no resistance)

$I_{ideal}=\frac{E}{R+r}=\frac{10}{48+1}=\frac{10}{49}\approx 0.20408A$

Step 4: Relative error

Relative error $=\frac{I_{ideal}-I_{actual}}{I_{ideal}}$

$=\frac{0.20408-0.2}{0.20408}\approx 0.01995\approx 2\%$

Step 5: Summary

Ammeter reading: $I_{actual}=0.2A$

Relative error due to its resistance: $\sim 2\%$