WHAT DOES A VOLTMETER READ ACROSS A POTENTIAL DIVIDER?
A voltmeter of finite resistance sits in parallel with the resistor it measures and lowers the resistance of that branch, so it always reads less than the unloaded divider would suggest. The effect is negligible only when the meter resistance is much larger than the resistor it is across, which is exactly what this question removes.
A 12 V supply of negligible internal resistance is connected across two 1 kΩ resistors in series. A voltmeter of resistance 1 kΩ is connected across the lower resistor. What does the voltmeter read?
Redraw the circuit with the meter in it before you use the divider formula. The meter is not an observer here; it is a component.
- the meter is in parallel with the lower 1 kΩ
- combined: 1⁄R = 1⁄1000 + 1⁄1000, so R = 500 Ω
- total circuit resistance = 1000 + 500 = 1500 Ω
- V across the lower branch = 12 × 500⁄1500 = 4 V
6 V is what you get if you ignore the voltmeter and split 12 V equally between two equal resistors. That is the reading an ideal voltmeter of infinite resistance would give, and it is the answer the question is built to attract. The meter resistance is stated, and a value is never stated in an ESAT question for decoration.
8 V is what you get if you put the parallel pair on the wrong side and read the voltage across the upper 1 kΩ instead. The larger share of the voltage now sits across the larger resistance, which is the upper one.
When a load equal to the resistor it sits across is added, that branch halves, so a 1 : 1 divider becomes 2 : 1 and the reading drops from one half to one third of the supply. Recognising the halving turns this into 12 ÷ 3 with no formula at all. As a rule of thumb, a meter ten times the resistance it measures costs you about 9% of the reading; a hundred times, about 1%.
THE GENERAL RULE
Any instrument connected into a circuit changes the circuit. A voltmeter goes in parallel and must have a high resistance to disturb it little; an ammeter goes in series and must have a low one. When a question gives you the meter’s resistance rather than calling it ideal, that number is the question, and the unloaded answer is on the option list waiting for you.
Updated · written to the published ESAT content specification