Electric Circuits
Beginner
Ohm's Law
Source: High school physics (Chinese)
Problem Sets:
ohm's law
Problem
A voltmeter with a full-scale range of 150 V has an internal resistance of $R_V = 20$ kΩ. It is connected in series with an unknown high resistance $R$, and this combination is connected across a 110 V supply. The voltmeter reads 5 V.
Find the value of the high resistance $R$. (This is one method for measuring a high resistance.)
$R = 4.2 \times 10^5 \,\Omega = 420$ kΩ
The voltmeter and unknown resistor are in series, so the same current flows through both.
The current through the circuit, determined from the voltmeter reading and its internal resistance:
$$I = \frac{U_V}{R_V} = \frac{5}{20 \times 10^3} = 2.5 \times 10^{-4} A.$$The voltage across the unknown resistor is the remainder of the supply voltage:
$$U_R = U - U_V = 110 - 5 = 105 V.$$By Ohm's law, the unknown resistance is
$$R = \frac{U_R}{I} = \frac{105}{2.5 \times 10^{-4}} = 4.2 \times 10^5 \,\Omega = 420 \text{ k}\Omega.$$