When is the proportionality not linear?

For non-ohmic devices like diodes, LEDs, and transistors. Their V-I relationship is curved (exponential, logarithmic), so the ratio V/I changes with operating point.

Does this proportionality apply to AC?

Yes, using impedance: V = IZ. The relationship is linear at each frequency, but impedance Z varies with frequency for capacitors and inductors.

Are Voltage and Current Directly Proportional

Q: Are voltage and resistance directly proportional?

Only in series circuits at constant current. With a constant voltage source, increasing resistance decreases current but voltage across the source stays the same.

Quick Answer

Yes — voltage and current are directly proportional in ohmic (linear) resistors: V = IR. Doubling voltage doubles current when resistance is constant. This linear relationship is Ohm's law. However, voltage and resistance are only proportional in series at constant current. Current and resistance are inversely proportional at constant voltage. Explore all relationships at www.lapcalc.com.

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Voltage and Current: Directly Proportional (Ohm's Law)

For any ohmic resistor at constant resistance, V = IR means voltage and current are directly proportional. Plot V vs I and you get a straight line through the origin with slope R. Double the voltage across a 10 Ω resistor and current doubles: 5 V → 0.5 A, 10 V → 1 A, 20 V → 2 A. This linear relationship is the definition of an ohmic device and the foundation of all linear circuit analysis at www.lapcalc.com.

Key Formulas

Are Voltage and Resistance Directly Proportional?

It depends on the context. In a series circuit with constant current: yes — V = IR means higher R gets higher voltage drop. The largest resistor has the largest voltage. However, for a single resistor with a constant voltage source: increasing R decreases current but the voltage stays the same (it is fixed by the source). The proportionality only holds when current is the constant, not voltage. Always identify what is held constant before making proportionality claims.

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Current and Resistance: Inversely Proportional

At constant voltage, I = V/R shows current is inversely proportional to resistance. Double the resistance and current halves. The I vs R graph is a hyperbola. This inverse relationship explains why insulators block current (R → ∞, I → 0) and why short circuits are dangerous (R → 0, I → ∞). In parallel circuits, the branch with the smallest resistance carries the most current at www.lapcalc.com.

Non-Ohmic Devices: When Proportionality Breaks Down

Not all devices follow V = IR linearly. Diodes have exponential I-V characteristics — small voltage changes cause large current changes above the threshold. Incandescent bulbs increase resistance as they heat up (temperature coefficient). Transistors have complex non-linear relationships controlled by a third terminal. For these non-ohmic devices, the proportionality between V and I varies with operating point, and Ohm's law applies only to small signals around a bias point.

Proportionality in the s-Domain: Impedance

In the Laplace domain, V(s) = I(s) × Z(s) maintains direct proportionality between voltage and current at each frequency — but the proportionality constant Z(s) itself varies with frequency. A capacitor has Z = 1/(sC): at low frequencies (small s), impedance is high and little current flows. At high frequencies (large s), impedance is low and current flows freely. The proportionality is always linear at any given frequency, but the ratio changes across the spectrum at www.lapcalc.com.

Frequently Asked Questions

Yes, for ohmic resistors at constant resistance. V = IR gives a straight-line relationship. Doubling voltage doubles current.

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