Converting a Galvanometer into a Voltmeter

Physics · Moving Charges And Magnetism · NEET

To turn a galvanometer into a voltmeter, connect a HIGH resistance R in SERIES with the galvanometer. Use R = V/Ig - G, where V is the max voltage you want to read, Ig is the full-scale deflection current, and G is the galvanometer resistance. Memory hook: "Voltmeter = Very high resistance in Series" (both start with V and S) - so a good voltmeter has near-infinite resistance and draws almost no current.
Galvanometer + high series resistance R = VoltmeterG12 to 100 ΩR (high)ABSame current Ig flows through G and R (in SERIES)V = Ig (R + G) → R = V/Ig − GConnect ACROSScomponent (parallelto what you measure)High R → tiny current→ no circuit disturbance
A galvanometer (resistance G) with a large resistance R in series becomes a voltmeter. The same full-scale current Ig flows through both, so V = Ig(R + G), giving R = V/Ig - G. The high total resistance means the voltmeter draws almost no current and is connected across the component being measured.

Your doubts, answered

Why do we add resistance in SERIES for a voltmeter but in PARALLEL (shunt) for an ammeter?

A voltmeter is connected across (in parallel with) a component, so it must NOT steal current from that component. Adding a large resistance in series makes the galvanometer's total resistance very high, so it draws almost no current and the circuit is barely disturbed. An ammeter goes in series in the main line, so it must have very LOW resistance - that is why the ammeter gets a small parallel shunt instead. Series-for-voltmeter, parallel-for-ammeter is the key rule.

What exactly is the formula and what does each letter mean?

R = V/Ig - G. Here V is the maximum voltage the voltmeter should read (its range), Ig is the current that gives full-scale deflection in the galvanometer, and G is the galvanometer's own resistance. The idea: at full scale the same current Ig flows through R and G in series, so V = Ig(R + G). Solve for R.

Why must a voltmeter have very HIGH resistance ideally?

An ideal voltmeter has infinite resistance so it draws zero current. If it drew current, it would change the very voltage it is trying to measure (loading effect). NCERT says we keep the disturbance below one per cent, so R is made large - typically thousands of ohms - and G becomes tiny compared to R.

Does the galvanometer resistance G matter after adding R?

Usually very little. Since R is very large and G is small, R + G is almost equal to R. That is why NCERT writes R + G ≈ R (large). But in NEET numericals you must still subtract G to get the exact series resistance: R = V/Ig - G, not just V/Ig.

How do I convert a voltmeter to a HIGHER range?

A higher range needs a larger series resistance. From R = V/Ig - G, if you want to read a bigger V (same galvanometer), R must increase. To make a multi-range voltmeter, use different series resistances, one for each range.

⚠️ The NEET trap
Using R = V/Ig as the answer and forgetting to subtract the galvanometer resistance G.
The correct series resistance is R = V/Ig - G. The total resistance V/Ig includes both R and G, so R alone is V/Ig minus G.
🧠 Total resistance = V/Ig. The SERIES piece you add is that total MINUS G. Read the question: it asks for the added resistance, not the total.

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Frequently asked

What is the formula to convert a galvanometer into a voltmeter?

R = V/Ig - G, where R is the high resistance added in series, V is the desired voltage range, Ig is the full-scale deflection current, and G is the galvanometer resistance.

Is the resistance connected in series or parallel?

In series. A high resistance in series makes the voltmeter's total resistance very high so it draws negligible current when connected across a component.

Why should an ideal voltmeter have infinite resistance?

So it draws zero current and does not disturb the circuit it measures. This avoids the loading error and gives the true voltage across the component.

How is converting to a voltmeter different from converting to an ammeter?

Voltmeter: add a HIGH resistance in SERIES (high total resistance). Ammeter: add a LOW resistance (shunt) in PARALLEL (low total resistance). They are opposite modifications.

Worked example: G = 12 ohm, Ig = 3 mA, range V = 18 V. Find R.

R = V/Ig - G = 18/0.003 - 12 = 6000 - 12 = 5988 ohm in series. Notice G (12) is tiny compared to R, so the voltmeter resistance is almost all R.