Question

Explain how the current in a circuit is related to the resistance in circuit.

Answer 1

The basic relationship between current and resistance in a circuit is given by Ohm’s law:

I = V / R

where
- I is the current (amperes, A),
- V is the voltage (volts, V) across the resistor or circuit,
- R is the resistance (ohms, Ω).

Key points
- For a fixed voltage, current is inversely proportional to resistance: increasing R reduces I, decreasing R increases I. Example: a 12 V source across 6 Ω gives I = 12/6 = 2 A; if R is doubled to 12 Ω, I = 1 A.
- For a fixed current source, the voltage will change to satisfy V = I·R.
- In real sources, include internal resistance r: I = V_emf / (R + r).

Series and parallel resistances
- Series: resistances add, R_total = R1 + R2 + ... ; larger R_total → smaller current for given V.
- Parallel: reciprocals add, 1/R_total = 1/R1 + 1/R2 + ... ; adding a parallel branch reduces R_total → increases current from the source.

Power dissipation
- Power dissipated in a resistor: P = V·I = I^2·R = V^2 / R. Higher resistance at fixed I gives more heat; at fixed V, higher R gives less current and thus less power.

Limitations
- Ohm’s law applies to ohmic (linear) components. Many devices (diodes, transistors, filament lamps) are non‑ohmic so I–V is not a simple V/R and resistance can vary with voltage, current, or temperature.
- Resistance itself can change with temperature or other conditions (metals typically increase R with temperature; some semiconductors decrease R).

Short summary: For a given voltage source, current falls as resistance increases (I = V/R); the detailed behavior in a circuit depends on how resistances are arranged and on whether components are ohmic.