Q.A voltmeter of resistance can measure up to 25 V. How will you convert it so that it can read up to 250 V?
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Start your 14-day free trial to unlock the full solution →To extend the range of a voltmeter from 25 V to 250 V, you must connect a high resistance in series with the existing meter. The required series resistance is .
Why this works: The core idea
A voltmeter is essentially a sensitive current-measuring device (a galvanometer) with a large fixed resistor in series. The pointer deflects fully when a specific current — the full-scale deflection current — flows through it. For the given voltmeter, that full-scale current is:
This current must never exceed , or the meter will be damaged. To measure a larger voltage (250 V), you need to limit the current to the same even when the applied voltage is ten times higher. The only way to do that is to add extra resistance in series — the current will then be , so a larger keeps at the safe value.
The galvanometer’s full-scale deflection current is the invariant in any voltmeter conversion. You never change the meter movement itself — you only add series resistance to drop the extra voltage.
Step-by-step solution
1. Find the full-scale deflection current of the existing voltmeter
The voltmeter has resistance and measures up to . The current that produces full deflection is:
This is the maximum current the meter can safely handle.
2. Determine the total resistance needed for the new range
You want the voltmeter to read up to . For the same , the total series resistance required is:
3. Calculate the extra series resistance to add
The existing voltmeter already contributes . So the additional resistance you must connect in series is:
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