Action and use of circuit components Revision Notes

In electrical circuits, three fundamental quantities are essential: current, potential difference, and resistance.

Current (I) is the rate of flow of electric charge through a conductor, measured in amperes (A).

Potential difference (V), also called voltage, is the energy transferred per unit charge between two points in a circuit, measured in volts (V). One volt equals one joule per coulomb (1 V = 1 J/C). It is measured using a voltmeter connected in parallel across the component of interest, such as a resistor or conductor. The voltmeter must have a very high resistance to avoid changing the current in the circuit when connected.

• Current (I) unit: ampere (A)
• Potential difference (V) unit: volt (V)
• Resistance (R) unit: ohm (Ω)

Resistance (R) is a measure of how much a conductor opposes the flow of electric current. It depends on the material, length, and cross-sectional area of the conductor.

When a current flows through a conductor, energy is transferred to the conductor's atoms, causing collisions that impede the flow of electrons. This opposition is quantified as resistance.

The higher the resistance, the more energy is required to push the same amount of current through the conductor, resulting in a higher potential difference across it.

• Resistance depends on material, length, and thickness
• Higher resistance means more opposition to current flow
• Energy transfer causes heating in resistors

Ohm's Law states that the potential difference (V) across a conductor is directly proportional to the current (I) flowing through it, provided the temperature remains constant.

Mathematically, Ohm's Law is expressed as: V = I × R

This means if the current is kept constant, increasing the resistance will increase the potential difference across the conductor proportionally, and vice versa.

• Ohm's Law formula: V = I × R
• V is in volts (V), I in amperes (A), R in ohms (Ω)
• Valid only if temperature and physical conditions are constant

Suppose a conductor carries a current of 2.0 A and has a resistance of 5.0 Ω. To find the potential difference across it, use Ohm's Law:

V = I × R = 2.0 A × 5.0 Ω = 10 V. The potential difference is 10 volts.

If the resistance increases to 8.0 Ω while the current remains at 2.0 A, the new potential difference is: V = 2.0 A × 8.0 Ω = 16 V, showing that voltage increases with resistance at constant current.

• Formula: V = I × R
• Substitution: V = 2.0 A × 5.0 Ω = 10 V
• Units: volts (V)
• Answer: 10 V potential difference
• Common error: forgetting to keep current constant or mixing units

To measure potential difference across a resistor, connect a voltmeter in parallel with the resistor in the circuit.

The ammeter, which measures current, must be connected in series with the resistor to measure the current flowing through it.

Ensure the voltmeter has a very high resistance to avoid drawing current and affecting the circuit operation, and the ammeter has very low resistance to avoid adding significant resistance to the circuit.

• Voltmeter connected in parallel across resistor
• Ammeter connected in series with resistor
• Voltmeter high resistance, ammeter low resistance

A variable potential divider consists of two resistors connected in series across a voltage source: one fixed resistor and one variable resistor (often a potentiometer). The total voltage from the source is divided between these two resistors according to their resistances.

The variable resistor is adjustable, allowing its resistance to be changed continuously within a certain range. The output voltage is taken across the variable resistor, making it possible to vary the output voltage smoothly from near zero volts up to nearly the full supply voltage.

A simple circuit diagram can be drawn as follows: Draw a voltage source (labelled V) with two resistors in series connected across it. Label the fixed resistor R₁ and the variable resistor R₂. The output voltage V_out is taken across R₂.

• Two resistors in series: one fixed (R₁), one variable (R₂).
• Connected across a voltage supply (V).
• Output voltage (V_out) taken across the variable resistor (R₂).

The potential divider rule states that the voltage across a resistor in a series circuit is proportional to its resistance.

Mathematically, for two resistors R₁ and R₂ in series across a voltage V, the output voltage across R₂ is given by:

\[ V_{out} = V \times \frac{R_2}{R_1 + R_2} \] where: V_out is the output voltage across R₂, V is the total voltage supplied, R₁ is the fixed resistor, and R₂ is the variable resistor.

• Output voltage depends on the ratio of R₂ to the total resistance.
• Increasing R₂ increases V_out; decreasing R₂ decreases V_out.
• This allows continuous control of output voltage by adjusting R₂.

When the variable resistor R₂ is adjusted, its resistance changes, altering the voltage drop across it. Since the resistors are in series, the same current flows through both.

The voltage drop across a resistor in a series circuit is given by Ohm's law:

\[ V = IR \] where I is the current and R is the resistance of that resistor. Increasing R₂ increases the voltage drop across it, thus increasing the output voltage taken across R₂. Conversely, decreasing R₂ reduces the voltage drop and output voltage.

• Current is constant through series resistors.
• Voltage divides according to resistance values.
• Adjusting R₂ changes voltage drop and output voltage.

Variable potential dividers are widely used in electronics to provide adjustable voltage levels. Common applications include:

Volume controls in audio equipment, where the output voltage controls signal amplitude.

Light dimmers, adjusting voltage to lamps to vary brightness (with suitable components). Sensor calibration circuits, where output voltage needs fine adjustment. Tuning circuits and variable biasing in amplifiers.

• Adjustable voltage output for control and calibration.
• Common in audio, lighting, and sensor circuits.
• Provides smooth, continuous voltage variation.

Suppose a 12 V supply is connected across a fixed resistor R₁ = 4 kΩ and a variable resistor R₂ = 8 kΩ in series. Calculate the output voltage across R₂.

Using the potential divider formula: \[ V_{out} = V \times \frac{R_2}{R_1 + R_2} = 12 \times \frac{8}{4 + 8} = 12 \times \frac{8}{12} = 8 \text{ V} \]

Therefore, the output voltage is 8 volts across the variable resistor when R₂ is 8 kΩ.

• Use potential divider formula.
• Substitute values carefully.
• Calculate output voltage in volts (V).

A potential divider is a simple circuit used to produce a fraction of an input voltage as an output voltage. It consists of two or more resistors connected in series across a voltage supply.

The total voltage from the supply is divided among the resistors in proportion to their resistances, according to Ohm's law and the rules for series circuits.

Potential dividers are widely used in electronics to obtain a desired voltage lower than the supply voltage, for example, to provide reference voltages or to adjust signal levels.

• Two resistors, R₁ and R₂, connected in series across a voltage supply V.
• Voltage across R₁ is V₁; voltage across R₂ is V₂.
• Total voltage V = V₁ + V₂.

In a series circuit, the current I is the same through all components. The voltage across each resistor depends on its resistance.

Ohm's law states V = IR, where V is voltage, I is current, and R is resistance.

Since current is constant, voltage across each resistor is proportional to its resistance: V₁ = IR₁ and V₂ = IR₂.

• Current I is the same through R₁ and R₂.
• Voltage divides according to resistance values.
• Total voltage V = I(R₁ + R₂).

From V₁ = IR₁ and V₂ = IR₂, dividing these gives: V₁ / V₂ = R₁ / R₂.

This formula shows that the ratio of voltages across the two resistors equals the ratio of their resistances.

This relationship is valid only when the resistors are connected in series and the current is the same through both.

• Formula: V₁ / V₂ = R₁ / R₂.
• Voltage ratio depends solely on resistance ratio.
• Useful for calculating unknown voltages or resistances.

To find the voltage across one resistor, use the total voltage and the resistance values.

Example: Given V = 12 V, R₁ = 2 kΩ, R₂ = 4 kΩ, find V₁ and V₂.

Step 1: Calculate total resistance R_total = R₁ + R₂ = 6 kΩ = 6000 Ω.

• Calculate current: I = V / R_total = 12 V / 6000 Ω = 0.002 A (2 mA).
• Calculate V₁: V₁ = IR₁ = 0.002 A × 2000 Ω = 4 V.
• Calculate V₂: V₂ = IR₂ = 0.002 A × 4000 Ω = 8 V.
• Check ratio: V₁ / V₂ = 4 V / 8 V = 0.5; R₁ / R₂ = 2000 Ω / 4000 Ω = 0.5, confirming the formula.

To draw a two-resistor potential divider: start with a horizontal line representing the voltage supply.

Draw two resistors in series connected between the positive and negative terminals of the supply.

Label the resistors R₁ and R₂, and mark the voltages across them as V₁ and V₂ respectively, with arrows indicating the voltage drop direction from positive to negative terminal of each resistor.

• Voltage supply symbol with + and – terminals.
• Resistors represented by zigzag lines labeled R₁ and R₂.
• Voltage drops V₁ and V₂ shown across R₁ and R₂ respectively.