Potential Dividers

The operation of a potential divider is governed by Kirchhoff's Second Law, which states that the sum of potential differences in a closed loop must equal the total electromotive force.

According to Ohm's Law ($V = IR$), since the current ($I$) is identical through all components in a series circuit, the voltage drop across each resistor is directly proportional to its resistance.

This proportionality means that the resistor with the highest resistance will always receive the largest share of the input voltage.

The mathematical relationship is expressed by the ratio: $\frac{V_1}{V_2} = \frac{R_1}{R_2}$, indicating that the voltage 'splits' exactly as the resistances do.

To calculate the output voltage across a specific resistor ($R_2$), use the Potential Divider Equation: $V_{out} = \frac{R_2}{R_1 + R_2} \times V_{in}$

Step 1: Identify the total resistance of the series circuit by summing all individual resistors ($R_{total} = R_1 + R_2 + ...$).

Step 2: Determine which resistor the output voltage is being measured across; this value becomes the numerator in your fraction.

Step 3: Multiply the ratio of the target resistance to the total resistance by the supply voltage to find the specific potential drop.

In a Potentiometer, a sliding contact moves along a resistive track, effectively changing the ratio of $R_1$ to $R_2$ and providing a continuously variable $V_{out}$ from $0$ to $V_{in}$.

When using an LDR (Light Dependent Resistor), increasing light intensity decreases its resistance, which subsequently decreases the voltage across it if it is the 'bottom' resistor ($R_2$).

The Ratio Shortcut: Instead of full calculations, use ratios. If $R_2$ is twice $R_1$, it will take two-thirds of the total voltage ($2:1$ ratio).

Sanity Check: Always verify that $V_{out}$ is less than $V_{in}$. If your calculation results in a higher voltage than the source, you have likely inverted the fraction.

Numerator Rule: Students often lose marks by putting the wrong resistor in the numerator; always use the resistor that is in parallel with the output terminals.

Directional Logic: In sensor questions, ask: 'If the physical quantity (light/heat) increases, does the resistance go up or down?' and then 'How does that change the share of voltage?'

Loading Effect: A common error is assuming $V_{out}$ remains constant when a low-resistance load is connected to the output; in reality, the load acts in parallel with $R_2$, reducing the effective resistance and lowering $V_{out}$.

Total Resistance Confusion: Ensure the denominator is the sum of all resistors in the series chain, not just the two used for the divider if others are present.

Inverse Relationships: Forgetting that for NTC thermistors and LDRs, the resistance decreases as the stimulus (temperature/light) increases, leading to incorrect predictions of voltage behavior.