Interpret the circuit

Two resistors are connected in series across a battery. One resistor is $500\,\Omega$, and the voltmeter of resistance $2000\,\Omega$ is connected across this $500\,\Omega$ resistor.

So, when the voltmeter is connected, the effective resistance across that branch becomes the parallel combination:

$R_p = \frac{500 \times 2000}{500 + 2000} = \frac{1000000}{2500} = 400\,\Omega$

Use the figure data

From the figure, the other series resistor is $600\,\Omega$ and the battery voltage is $20\,\text{V}$.

Thus the circuit becomes:

• one resistor: $600\,\Omega$
• other branch (effective): $400\,\Omega$

Total resistance:

$R_{\text{total}} = 600 + 400 = 1000\,\Omega$

Find the circuit current

$I = \frac{V}{R_{\text{total}}} = \frac{20}{1000} = 0.02\,\text{A}$

Find voltmeter reading

The voltmeter reads the voltage across the parallel branch of equivalent resistance $400\,\Omega$:

$V_p = I \times R_p = 0.02 \times 400 = 8\,\text{V}$

Hence the voltmeter reading is:

$\boxed{8\,\text{V}}$

Compare with stored answer

Stored correct answer = $8$

Our derived answer = $8$

So they agree.