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Question: A voltmeter having a resistance of 998 ohms is connected to a cell of e.m.f. 2 volt and internal res...

A voltmeter having a resistance of 998 ohms is connected to a cell of e.m.f. 2 volt and internal resistance 2 ohm. The error in the measurement of e.m.f. will be

A

4×10−14 \times 10 ^ { - 1 } volt

B

C

4×10−34 \times 10 ^ { - 3 } volt

D

2×10−12 \times 10 ^ { - 1 } volt

Answer

4×10−34 \times 10 ^ { - 3 } volt

Explanation

Solution

Error in measurement = Actual value – Measured value

Actual value = 2V

i=2998+2=1500Ai = \frac { 2 } { 998 + 2 } = \frac { 1 } { 500 } A

Since E=V+irE = V + i r ⇒ V=E−ir=2−1500×2=998500VV = E - i r = 2 - \frac { 1 } { 500 } \times 2 = \frac { 998 } { 500 } V

∴ Measured value =998500 V= \frac { 998 } { 500 } \mathrm {~V}

⇒ Error =2−998500=4×10−3= 2 - \frac { 998 } { 500 } = 4 \times 10 ^ { - 3 } volt