A voltmeter of internal resistance x Ω has a maximum measuring range of 20 V. To increase its maximum range to 30 V without changing the full-scale current through the meter movement, what modification is required?
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Question

A voltmeter of internal resistance x Ω has a maximum measuring range of 20 V. To increase its maximum range to 30 V without changing the full-scale current through the meter movement, what modification is required?

Options

G1 Physics · Accepted Answer

The full-scale current of the voltmeter is I(full) = 20 ÷ x. To obtain a 30 V range by adding a series resistance R, the same full-scale current must satisfy 20 ÷ x = 30 ÷ (x+R). Therefore, 20(x+R) = 30x. So, 20R = 10x, R = x ÷ 2. The extra resistance must be connected in series. Correct option: A.