§ 10.1 Practical circuits
Key ideas
- EMF is the energy supplied per unit charge by a source; it is what a real battery would deliver with no current flowing.
- A real source has internal resistance r: the terminal p.d. is V = E − Ir, with Ir the "lost volts".
- Plot terminal p.d. against current: the intercept is E and the gradient magnitude is r.
Equations
V = E − I rterminal p.d. = EMF − the volts lost across rV
Fig. 1 · V = E − Ir as a graph: with no current the battery shows its full EMF; every extra ampere drops r volts inside the battery itself.
Watch out: a voltmeter across a battery in use reads the terminal p.d., not the EMF. The EMF only appears when the current is (effectively) zero: open circuit or a perfect voltmeter alone.
§ 10.2 Kirchhoff's laws
Key ideas
- First law: the currents into a junction equal the currents out; charge is conserved.
- Second law: around any closed loop, the sum of EMFs equals the sum of the IR drops; energy is conserved.
- Series resistors add, R = R1 + R2; parallel resistors add as reciprocals, 1/R = 1/R1 + 1/R2, giving less than the smallest branch.
Equations
ΣI in = ΣI outfirst law: charge conservation at a junctionA
ΣE = ΣIRsecond law: energy conservation round a loopV
Fig. 2 · Kirchhoff's first law at the junction: whatever current arrives must leave. Around each loop, the EMF equals the sum of the IR drops crossed.
Watch out: adding a resistor in parallel lowers the combined resistance: it opens another path for current. Two 10 Ω resistors in parallel make 5 Ω.
§ 10.3 Potential dividers
Key ideas
- Two resistors in series share the supply p.d. in the ratio of their resistances.
- Swap one resistor for a thermistor or LDR and the output voltage tracks temperature or light level: the basis of sensor circuits.
- A potentiometer is a continuously variable divider; in null methods it is balanced until a galvanometer reads zero.
Equations
Vout = Vin × R2/(R1 + R2)the share across R2 when the output is unloadedV
Fig. 3 · The divider hands R2 its share of the input. If R2 is a thermistor, warming it lowers its resistance and Vout falls: a temperature sensor in two components.
Watch out: the divider equation assumes the output draws no current. Connect a low-resistance load across R2 and the effective resistance drops, pulling Vout below the formula's value.