Current, Voltage, and Resistance

Current is the rate of flow of electric charge.

$\boxed{I = \frac{Q}{t}}$

Where:

• $I$ = current (amperes, A)
• $Q$ = charge (coulombs, C)
• $t$ = time (seconds, s)

1 ampere = 1 coulomb per second (1 A = 1 C/s)

Key Points

• Current is caused by the flow of electrons (in metals) or ions (in solutions)
• Conventional current flows from positive to negative (historical convention)
• Electron flow is from negative to positive (actual flow in metals)
• Current is measured with an ammeter connected in series

Potential difference (p.d. or voltage) is the energy transferred per unit of charge.

$\boxed{V = \frac{E}{Q}}$

Where:

• $V$ = potential difference (volts, V)
• $E$ = energy transferred (joules, J)
• $Q$ = charge (coulombs, C)

1 volt = 1 joule per coulomb (1 V = 1 J/C)

Key Points

• Voltage drives the current — it's the "push" that moves charges
• Measured with a voltmeter connected in parallel across the component
• The battery provides the voltage (EMF — electromotive force)
• Voltage is "used up" across components in a circuit

Resistance is the opposition to the flow of current.

$\boxed{V = I \times R}$

(This is Ohm's Law — valid for ohmic conductors at constant temperature)

Where:

• $V$ = potential difference (V)
• $I$ = current (A)
• $R$ = resistance (ohms, Ω)

Rearranging

$I = \frac{V}{R} \qquad R = \frac{V}{I}$

Defining the Ohm

1 ohm is the resistance when a p.d. of 1 V causes a current of 1 A.

$1 \text{ Ω} = 1 \text{ V/A}$

What Causes Resistance?

• Electrons collide with positive ions in the metal lattice
• These collisions transfer energy (heating the wire)
• More collisions = higher resistance

Factors Affecting Resistance of a Wire

$R = \frac{\rho L}{A}$

Ohm's Law: For an ohmic conductor (at constant temperature), the current is directly proportional to the potential difference.

I-V Graphs

Ohmic conductor (resistor at constant temp): Straight line through origin. Resistance is constant.

Filament lamp: Curved line. As current increases, the filament heats up, resistance increases. Curve gets shallower.

Diode: Almost no current flows in reverse direction. In forward direction, current flows once threshold voltage (~0.7 V) is reached. Very low resistance in forward bias.

Required Practical: I-V Characteristics

1. Set up a circuit with the component, ammeter (series), voltmeter (parallel), and variable resistor
2. Adjust the variable resistor to change the current and voltage
3. Record I and V readings
4. Reverse the battery connections and repeat (for negative values)
5. Plot an I-V graph

• Current $I = Q/t$ (amperes) — rate of flow of charge
• Voltage $V = E/Q$ (volts) — energy per unit charge
• Resistance $R = V/I$ (ohms) — opposition to current
• Ohm's Law: $V = IR$ (for ohmic conductors at constant temperature)
• Ammeter in series; voltmeter in parallel
• I-V graphs: linear for ohmic resistors, curved for lamps, one-way for diodes