IB Physics HL B.5 Current and circuits Notes

A cell is an energy source in a circuit. It raises the energy of charges by doing work on them inside the source. Components such as resistors and lamps then take energy from the charges. This energy-per-charge language is the clean way to distinguish emf from potential difference.

Define emf and explain how a chemical cell provides energy to charges in a circuit.

Chemical cells and solar cells are both electrical energy sources because they do work on charges. A chemical cell uses chemical reactions to transfer energy to charge carriers; a solar cell uses incident light to transfer energy to charge carriers. The source provides an emf, meaning energy supplied per unit charge, so epsilon = E/Q and the unit is the volt. In a closed circuit the charges then move through external components, where the electrical energy is transferred to other forms such as heating in a resistor or light in a lamp. Do not say the source creates charge: charge is already present in the circuit, and the source supplies energy to move it around the loop.

Compare how a chemical cell and a solar cell act as energy sources in a circuit.

Resistance measures how much a component opposes charge flow and how much energy is transferred for each coulomb of charge passing through it. Use R = V/I, with V taken across the component and I taken through that same component. The unit is the ohm, Ω. In a metal, free electrons drift through a lattice of positive ions; collisions with vibrating ions transfer energy to the lattice, so electrical energy becomes internal energy. Be careful with graphs: the gradient of a V-I graph is resistance, but the gradient of an I-V graph is 1/R. A non-ohmic component can still have a resistance V/I at a point even if that value changes as current or temperature changes.

A student says resistance is just the gradient of any current-voltage graph. Explain what is wrong with this statement.

Ohm's law is a condition-based statement, not just the equation V = IR. A conductor is ohmic when the current through it is directly proportional to the potential difference across it, provided temperature and other physical conditions stay constant. In that case R = V/I has the same value at different operating points, and the I-V characteristic is a straight line through the origin. If the component heats up, as in a filament lamp, lattice ions vibrate more strongly, electron collisions increase, and the resistance changes. Then the graph curves and the component is non-ohmic even though R = V/I can still be calculated at a point.

A metal wire has a straight I-V graph through the origin when the current is small, but the graph curves at larger currents. Explain this behaviour.

Power tells you how quickly energy is transferred. The defining equation is P = E/t, so one watt is one joule per second. In an electrical component, P = IV because current is charge flow per second and potential difference is energy transferred per coulomb. Always match the current through the component with the potential difference across that same component. If the component resistance is also involved, combine P = IV with V = IR to get P = I^2R or P = V^2/R. These forms are algebraically equivalent only when the I, V, and R refer to the same operating point of the same component.

A resistor is connected to a power supply. Explain how to choose between P = IV, P = I^2R, and P = V^2/R in an exam calculation.

Electrical energy transfer follows directly from the definition of potential difference. A potential difference of V means each coulomb of charge transfers V joules of energy, so E = QV. If a steady current I flows for time t, then Q = It, giving E = IVt. This is the same as E = Pt when P = IV. The equation must use values for the same component over the same time interval. In exam explanations, add the energy pathway: for example, charges transfer electrical energy to a resistor, increasing its internal energy.

A student writes E = IVt for every circuit energy question. Explain when this is valid and how it is related to E = QV.

An electric cell is an energy source. Chemical reactions inside the cell transfer energy to charges, so the cell provides an emf: energy supplied per unit charge. In circuit diagrams the longer line marks the positive terminal and the shorter line marks the negative terminal. Conventional current in the external circuit is drawn from the positive terminal to the negative terminal, while electrons in a metal drift the opposite way. A battery is two or more cells; if cells are connected in series and face the same direction, their emfs add. If one cell is reversed, its emf opposes the others.

Two identical 1.5 V cells are connected in series to a lamp. State the total emf if the cells face the same way, and explain what changes if one cell is reversed.

The circuit model uses conventional current, the direction positive charge would move. In the external part of a simple circuit, draw conventional current leaving the positive terminal of the cell, passing through components, and returning to the negative terminal. In metal wires the actual mobile charges are electrons, so their drift is opposite to the conventional-current arrow. This does not mean current is used up: charge circulates around a closed loop, while energy is supplied by the source and transferred in components such as lamps and resistors. If the loop is broken by an open switch, there is no steady current.

A student says the current is smaller after a lamp because the lamp uses up charge. Explain the correct circuit model.

Electric current tells you how quickly charge passes a point in a circuit. The definition is I = ΔQ/Δt, where ΔQ is the charge that crosses a boundary during time Δt. One ampere means one coulomb per second. If the current is steady, the charge transferred in time t is Q = It. The moving charge carriers depend on the material: in a metal they are free electrons, while in an electrolyte both positive and negative ions can carry charge. Keep the meanings separate: current is charge flow; energy transfer is found when that charge moves through a potential difference.

An ammeter reads 0.25 A in a metal wire for 2.0 minutes. Calculate the charge that passes a point and identify the mobile charge carriers.

Direct current and alternating current are distinguished by direction, not just by whether the current is changing. In DC, charge flow has one direction in the external circuit; the current may be steady or may vary in magnitude, but it does not reverse. In AC, the current reverses direction periodically. On a current-time graph, choose a positive direction: values above zero represent current in that direction and values below zero represent current in the opposite direction. An AC waveform crosses zero and changes sign repeatedly; its period is the time for one full cycle and its frequency is the number of cycles per second.

A current-time graph oscillates between +0.40 A and -0.40 A with a period of 0.020 s. State whether the current is DC or AC and calculate its frequency.

Kirchhoff's laws are conservation laws for circuits. At a junction, charge cannot accumulate in steady operation, so the rate of charge flow in equals the rate out: the total current entering equals the total current leaving. Around a closed loop, energy per unit charge is conserved: charges gain energy per coulomb at sources and lose energy per coulomb across components, so the sum of emf rises equals the sum of potential drops. When setting up equations, choose directions consistently. If a calculated current is negative, it usually means the real current is opposite to your assumed arrow.

At a junction, 0.60 A enters and two branch currents leave. One branch current is 0.25 A. In a separate loop, a 6.0 V source supplies two series components, one with a 2.0 V drop. Find the missing current and missing potential drop, stating the Kirchhoff rule used each time.

Resistance and resistivity are related but not the same. Resistivity ρ describes how strongly a material opposes current; resistance R describes a particular conductor made from that material. For a uniform conductor at constant temperature, R = ρL/A. Increasing the length gives charge carriers more lattice to move through, so resistance increases. Increasing the cross-sectional area gives more parallel paths for charge carriers, so resistance decreases. For a circular wire, remember A = πr^2: changing radius has a squared effect on area and therefore on resistance.

A wire is replaced by another wire of the same material at the same temperature. The new wire has twice the length and twice the radius. Determine the change in resistance.

Series and parallel rules come from Kirchhoff's laws. Components in series share one path, so charge has no branch choice and the same current passes through each component. The source potential difference is shared between the series components, and the resistances add. Components in parallel are connected across the same two nodes, so each branch has the same potential difference. Current splits between the branches, and adding a parallel branch lowers the total resistance because it provides another path for charge flow. To measure circuits without changing them much, place an ammeter in series with very low resistance and a voltmeter in parallel with very high resistance.

Two resistors, 4.0 Ω and 6.0 Ω, are connected first in series and then in parallel to the same supply. Compare the total resistance in the two arrangements and state one current or voltage rule for each.

Emf is the energy supplied per unit charge by the source. A real cell also has internal resistance, so some of that energy per charge is transferred inside the cell when current flows. The internal potential drop is Ir, called the lost volts. The voltage available to the external circuit is therefore the terminal potential difference, V = ε - Ir. If the external circuit is a resistance R, then V = IR, so ε = I(R + r). As current increases, lost volts increase and terminal pd decreases. On a graph of terminal pd V against current I, the intercept at I = 0 gives the emf and the gradient is negative, with magnitude equal to the internal resistance.

A graph of terminal potential difference V against current I for a cell is a straight line with intercept 1.50 V and gradient -0.30 V A^-1. State the emf and internal resistance, and explain why terminal pd decreases as current increases.

Variable resistance lets a circuit respond to conditions or user adjustment. An NTC thermistor decreases in resistance when temperature increases, and an LDR decreases in resistance when light intensity increases. A potentiometer changes resistance using a sliding contact, so it can continuously vary an output voltage. In a potential divider, the output depends on the ratio of resistances, not just on whether one resistance has increased or decreased. If the output is taken across the lower resistor R2, then Vout = Vin R2/(R1 + R2). Therefore, if R2 is an NTC thermistor and temperature rises, R2 decreases and Vout across it decreases. If the output were instead across the fixed resistor, the trend would be opposite.

An LDR is used as the lower resistor in a potential divider, and the output voltage is measured across the LDR. Explain what happens to the output voltage when light intensity increases.

Retrieve B.5 as one connected model. A source gives energy per coulomb to charges; current describes how much charge passes per second; components receive energy according to their potential difference and power. Resistance links voltage and current, while material geometry sets resistance through resistivity. Series and parallel rules come from Kirchhoff's charge and energy conservation. Real cells lose some voltage internally, and variable resistors such as thermistors, LDRs, and potentiometers change the circuit by changing resistance or a voltage-divider ratio.