(c) Energy and voltage in circuits

Domestic lights are connected in parallel. Each lamp receives the mains voltage, each branch can be switched independently, and one failed lamp does not break the paths through the other lamps.

The nature of a component matters because its resistance may not stay constant. For example, a filament lamp becomes hotter as current rises, so its resistance changes; the current is therefore set by the behaviour of the whole series circuit, not just by the number of components.

Use a variable power supply or a variable resistor to change the voltage. Record paired ammeter and voltmeter readings over a safe range, switch off between readings when temperature must be controlled, and repeat readings. Reverse the supply to obtain negative-voltage data, then plot voltage on the x-axis and current on the y-axis.

A longer connecting cable has a greater resistance than a similar short cable. With the same supply voltage, the charging current is smaller, so transferring the same charge takes longer.

The reverse changes also apply: in dimmer light an LDR has greater resistance, and at lower temperature the thermistor has greater resistance. These relationships are generally non-linear, so equal changes in light or temperature do not have to produce equal resistance changes.

Placed in an appropriate part of a circuit, the indicator can show that the path is complete or that a protected section is still carrying current.

Example: a 73 $\Omega$ resistor carries 7.8 mA. Convert $7.8 mA = 0.0078 A$, then $V = IR = 0.0078 \times 73 = 0.57 V$ to two significant figures.

A current of 3 A means that 3 coulombs of charge pass the point every second. If the rate is larger, more charge passes each second.

Example: a lamp carries 0.48 A for 30 s. $Q = It = 0.48 \times 30 = 14.4 C$, so about 14 C is transferred to two significant figures.

A metal contains positive ions fixed in a lattice and electrons that can move through the structure. When a voltage is applied, these mobile electrons gain a net drift through the metal, so charge is transferred along the conductor.

Current is a rate of charge flow. Charge is conserved, so in a steady circuit charge does not continually build up or disappear at the junction; the incoming flow rate must equal the combined outgoing flow rates.

Example: 0.60 A enters a junction. If one branch carries 0.20 A, the other carries $0.60 - 0.20 = 0.40 A$. The check is $0.20 + 0.40 = 0.60 A$.

Each branch begins and ends at the same pair of electrical points. A unit of charge therefore undergoes the same energy change between those points, whichever branch it follows.

If two resistors are each connected directly across a 4.5 V cell, the voltage across each resistor is 4.5 V. The currents in the two branches may still be different because their resistances may differ.

Example: 200 $\Omega$ and 400 $\Omega$ resistors are connected in series across 12 V. $R_{total}=600 \Omega$, so $I=V/R=12/600=0.020 A$. Then $V_1=IR_1=0.020 \times 200=4.0 V$ and $V_2=0.020 \times 400=8.0 V$.

Check both conservation rules: the same 0.020 A is used for each resistor, and $4.0 + 8.0 = 12 V$. The larger resistance receives the larger share of voltage in this series circuit.

A voltage of 6 V means that 6 joules of energy are transferred for every coulomb of charge that passes between the two points. If 2 C passes, the energy transferred is 12 J.

Example: 3.7 J is transferred when 4.3 mC passes. Convert $4.3 mC = 0.0043 C$, then $V=E/Q=3.7/0.0043=860 V$ to two significant figures.