← Electrical Systems

3 DC circuits

Watch: DC circuits Opens a YouTube search: pick a video that clicks for you Ohm’s law & power V=IR\qquad P=VI=I^2R=\frac{V^2}{R} The three power forms: pick the one matching your known quantities. Resistors in series R<sub>T</sub> = R₁ + R₂ + … Same current through each; voltages add. Resistors in parallel \frac{1}{R_T}=\frac{1}{R_1}+\frac{1}{R_2}+\cdots Same voltage across each; currents add.

EMF, terminal voltage and internal resistance

  • Every real battery has an EMF ε (the total energy per coulomb it can supply) AND an internal resistance r.
  • Terminal voltage VT = ε − Ir — always LESS than the EMF once current flows, because some voltage is "lost" driving current through r.
  • As a battery ages, r increases. The EMF barely changes, but more voltage is lost internally, so VT falls.
  • A voltmeter across an UNLOADED battery (no current flowing) reads the EMF directly, since Ir = 0 when I = 0.
Worked example Terminal voltage — "show that" A battery has EMF 9.00 V and internal resistance 0.200 Ω. When connected to a circuit, the current is 1.50 A. Show that the terminal voltage is 8.70 V. V_T = ε − Ir. V_T = 9.00 − (1.50 × 0.200). V_T = 9.00 − 0.300 = 8.70 V. ✓ V_T = 8.70 V. ✕

Terminal voltage is NOT the EMF, once current flows

A "show that" question wants unrounded values carried through (see Reading the notation), and it is common to write V = ε by mistake. The two are equal ONLY when I = 0 — an open circuit, or a voltmeter (which draws negligible current) across an unloaded cell. The moment current flows, VT = ε − Ir is strictly less than ε.

Series vs parallel: what is shared

  • Ask "what is the SAME here?" before choosing a rule.
  • Series: the same CURRENT flows through every component. Voltages add; resistances add.
  • Parallel: the same VOLTAGE is across every branch. Currents add; reciprocals of resistance add.
  • Adding a resistor in PARALLEL always DECREASES total resistance — a new path for current, like adding a lane to a road.

Practise just this