Electricity and Circuits: Voltage, Current, and Resistance
Electricity powers everything from light bulbs to smartphones. Understanding how charge flows through circuits — and the relationships between voltage, current, and resistance — unlocks the physics behind nearly every electronic device.
Electric Charge and Current
All matter contains electrically charged particles. Electrons carry a negative charge; protons carry a positive charge. In most solid materials, protons are fixed in the atomic lattice while electrons can move. When electrons flow through a conductor in a consistent direction, the result is an electric current.
Current (symbol I) is measured in amperes (A, or "amps"). One ampere equals one coulomb of charge passing a point per second. Conventional current is defined as flowing from the positive terminal of a source to the negative terminal — the opposite of the direction electrons actually move, a historical convention that persists because the mathematics works out the same either way.
Voltage
Voltage (symbol V), also called potential difference or electromotive force (EMF) when referring to a source, is the energy per unit charge driving charges around a circuit. It is measured in volts (V). Think of voltage as analogous to water pressure in a pipe: higher voltage pushes more charge through the circuit, just as higher pressure drives more water flow. A 9-volt battery provides 9 joules of energy per coulomb of charge that flows through it.
Resistance
Resistance (symbol R) is a material's opposition to the flow of current, measured in ohms (Ω). A material resists current because electrons collide with atoms in the lattice as they move. These collisions convert electrical energy to heat — which is how toasters and incandescent light bulbs work. Good conductors (copper, silver, aluminium) have very low resistance; insulators (rubber, glass, plastic) have extremely high resistance; semiconductors (silicon, germanium) fall in between and can be precisely engineered.
Resistance depends on the material's resistivity, its length, and its cross-sectional area: a longer, thinner wire has higher resistance than a short, thick one of the same material.
Ohm's Law
The relationship between voltage, current, and resistance was established experimentally by Georg Ohm in 1827. Ohm's Law states:
V = I R
Voltage = current × resistance. This can be rearranged: I = V / R and R = V / I. For a conductor that obeys Ohm's Law ("ohmic" conductor), the current is directly proportional to voltage if resistance is constant.
Worked example: A resistor is connected to a 12 V battery and draws a current of 0.5 A. What is its resistance?
R = V / I = 12 / 0.5 = 24 Ω
Series Circuits
In a series circuit, components are connected in a single loop so the same current flows through each one. Adding more components increases total resistance and reduces the current drawn from the source.
- Total resistance: Rtotal = R1 + R2 + R3 + …
- Current: the same through every component (I = Vtotal / Rtotal)
- Voltage: splits across components in proportion to their resistance (V1 = I × R1, and so on)
The key disadvantage of series circuits: if one component fails (e.g., a bulb burns out), the circuit is broken and all components stop working. Old-style Christmas tree lights wired in series had this problem.
Parallel Circuits
In a parallel circuit, components are connected across the same two nodes, giving each its own separate path for current. Adding more branches reduces total resistance and increases total current.
- Total resistance: 1/Rtotal = 1/R1 + 1/R2 + 1/R3 + … (total is always less than the smallest individual resistance)
- Voltage: the same across every branch (equal to the supply voltage)
- Current: splits between branches in inverse proportion to resistance (more current through the lower-resistance branch)
Household wiring uses parallel circuits: each appliance receives the full mains voltage and can be switched independently. If one lamp fails, others continue working.
For exactly two resistors in parallel, the total resistance simplifies to the product divided by the sum: Rtotal = (R1 × R2) / (R1 + R2). For example, 6 Ω and 12 Ω in parallel: Rtotal = (6 × 12) / (6 + 12) = 72/18 = 4 Ω.
Electrical Power
Power is the rate at which energy is transferred. In an electrical circuit:
P = IV
Power (watts) = current (amps) × voltage (volts). Substituting Ohm's Law gives two useful equivalent forms: P = I²R and P = V²/R.
Worked example: A 60-watt light bulb operates at 230 V. What current does it draw?
I = P / V = 60 / 230 ≈ 0.26 A
Energy consumed equals power multiplied by time: E = P × t. A 1000-watt (1 kW) appliance running for one hour uses 1 kilowatt-hour (kWh) of electrical energy — the unit used on electricity bills. One kWh = 3.6 × 106 J.
Kirchhoff's Laws
For more complex circuits, two rules attributed to Gustav Kirchhoff (1845) allow systematic analysis:
- Kirchhoff's Current Law (KCL): the sum of currents entering a junction equals the sum leaving it. Charge is conserved — it cannot accumulate at a node.
- Kirchhoff's Voltage Law (KVL): the sum of all voltage drops around any closed loop in a circuit equals zero. Energy is conserved — the energy supplied by sources equals the energy dissipated by resistors around any loop.
Summary
Electric current is the flow of charge, measured in amperes. Voltage (volts) is the energy per unit charge driving the current. Resistance (ohms) opposes current flow. Ohm's Law (V = IR) relates all three. Series circuits share the same current but split voltage; parallel circuits share the same voltage but split current. Electrical power P = IV, and energy = power × time. Kirchhoff's laws extend Ohm's Law to complex multi-loop circuits by enforcing conservation of charge and energy at every junction and loop.