Power, Energy & Passive Sign Convention

Multiply voltage by current and you get power — but the sign tells you whether a device is consuming or delivering energy.

Circuit AnalysisElectrical Engineering Year 1Free preview

⏱️ About 13 min

A phone charger warms up while charging your phone — one device is delivering energy, the other is receiving it. How do you tell which is which with just numbers?

💡

The big idea: Power in a circuit is simply voltage times current, and a single sign convention — the passive sign convention — tells you whether any element is absorbing or supplying that power.

🎯 By the end, you'll be able to

Calculate instantaneous power from voltage and current using p = vi
Apply the passive sign convention to determine whether an element absorbs or supplies power
Compute energy transferred over a time interval given power
Verify power conservation in a simple circuit (total power supplied equals total power absorbed)

📎 Helpful to know first

Charge, Current & Voltage

Power: the product of push and flow

In circuits, power is the rate at which energy is transferred. Since voltage is energy per unit charge (J/C) and current is charge per unit time (C/s), their product gives energy per unit time — power:

The SI unit of power is the watt (W), where 1 W = 1 J/s = 1 V·A.

\[ p(t) = v(t)\,i(t) \]

Instantaneous power p (watts, W) equals voltage v (volts, V) times current i (amperes, A). This is the most used equation in circuit analysis.

The passive sign convention

The product p = vi gives a magnitude, but does it mean the element is absorbing power or supplying it? To resolve this, we use the passive sign convention:

If the current reference arrow enters the positive voltage terminal, then p = vi is the power absorbed by the element. A positive result means the element is indeed absorbing power; a negative result means it is actually supplying power to the rest of the circuit.

If the current arrow enters the negative terminal instead, then p = vi represents power supplied, and the absorbed power is -vi.

Left: passive sign convention — current enters the + terminal, so p = vi is power absorbed. Right: current enters the - terminal, so absorbed power is p = -vi.

🔑 The sign tells you everything

Once you consistently apply the passive sign convention, the sign of p automatically tells you the element's role:

p > 0 → element absorbs power (load, like a resistor or a charging battery)
p < 0 → element supplies power (source, like a battery or generator)

In any complete circuit, the total power absorbed equals the total power supplied — this is a statement of energy conservation and is a powerful checking tool.

📝 Worked example: A circuit element has terminals a and b. The voltage V_ab = 8 V (terminal a is at higher potential). A current of 1.5 A flows from terminal a to terminal b through the element (entering the + terminal). (a) Find the power absorbed by the element. (b) Find the energy consumed in 2 minutes of operation.

Current enters the positive terminal (a), so the passive sign convention applies directly: P = VI.
P = (8 V)(1.5 A) = 12 W. The positive result confirms the element absorbs 12 W.
Energy: W = P × t = 12 W × 120 s = 1440 J.

✓ The element absorbs 12 W of power and consumes 1440 J of energy in 2 minutes.

✏️ Practice: A circuit element has a voltage of 9 V (positive terminal on the left). A current of 0.3 A flows from right to left, entering the negative terminal. Calculate the power absorbed by the element in watts.

Solution

The current enters the negative terminal, so absorbed power is P = -VI.
P = -(9 V)(0.3 A) = -2.7 W.
The negative value means the element is actually supplying 2.7 W, not absorbing it.

Check your understanding

1. A circuit element has V = 10 V (+ on top) and I = 2 A flowing upward into the + terminal. How much power does the element absorb?

Current enters the positive terminal, so the passive sign convention applies: P = VI = 10 × 2 = 20 W. The result is positive, confirming the element absorbs 20 W.

2. Using the passive sign convention, an element has a calculated absorbed power of -15 W. What does this mean?

Under the passive sign convention, a negative absorbed power means the element is not absorbing but rather supplying power. The magnitude 15 W is the power delivered to the rest of the circuit.

✅ Key takeaways

Instantaneous power is p = vi, with units of watts (1 W = 1 V·A = 1 J/s).
The passive sign convention: if current enters the + terminal, p = vi is power absorbed.
Positive absorbed power means the element is a load; negative means it is a source.
Energy over a time interval is w = ∫p dt; for constant power, W = P × t.

➡️ With power and the sign convention in hand, the next lesson introduces the fundamental circuit elements — resistors, voltage sources, and current sources — whose voltage-current relationships bring these definitions to life.

Want to test yourself on this? Try the Electrical Aptitude test →