Direct current circuits AS Physics 2nd edition pp214-227

Current rules At any junction in a circuit, the total current leaving the junction is equal to the total current entering the junction Charge is conserved – no build up of charge in circuit Kirchoff’s first law or Kirchoff’s current law The current entering any junction is equal to the current leaving that junction. i2 + i3 = i1 + i4

Components in series The current entering a component is the same as the current leaving the component. The current passing through two or more components in series is the same through each component

Potential difference rules For any loop in a circuit, the sum of the emf’s equals the sum of the potential differences Energy is conserved– the energy from a circuit is equal to the energy input into a circuit Kirchoff’s second law or Kirchoff’s voltage law or The sum of all the voltages around a loop is equal to zero. v1 + v2 + v3 - v4 = 0

Component rules For two or more components in series, the total pd across all the components is equal to the sum of their potential differences across each component The pd across components in parallel is the same

Resistors in series The total resistance of a number of resistors in series is the sum of the individual resistors

Resistors in parallel N.B. Conductance = 1/Resistance

Resistive heating

Electromotive force EMF, emf, symbol ε The emf of a source is the energy per unit charge exerted on a circuit by the source ε=E/Q The terminal pd is less than the emf when ever a current flows through the source The terminal pd is the electrical energy per unit charge available from the source https://commons.wikimedia.org/w/index.php?curid=2525521

Internal resistance The internal resistance, r, of a source is due to the opposition to the flow of current through the source The internal resistance causes electrical energy, input by the source, to be dissipated as thermal energy, inside the source The internal resistance of a source is the loss of potential difference per unit current through the source The bigger the current the smaller the terminal p.d.

Emf and internal resistance ε = IR +Ir = V + Ir r = internal resistance I = current R = resistance in external circuit Often the internal resistance is shown as a resistor in series with a cell

Power Power delivered by the source, P = I ε I ε = I2R + I2r Power delivered by the cell = power delivered to the circuit + power dissipated in cell due to internal resistance Power delivered to R =

Power delivery in circuits

Measurement of internal resistance V = -Ir + ε Change R to change I Measure V Plot I vs V C.f. y = mx + c Gradient = -r y-intercept = ε Note ε = V when I = 0!

Circuits with identical cells in parallel For a circuit with n cells in parallel the current through each cell is so the pd lost in each cell is The terminal pd across each cell, Each time an electron passes through the cells it travels through only one cell therefore the cells act as a source of emf , ε and internal resistance,

N.B. Total internal resistance of identical cells in parallel = c.f. (compare with) Same result!

Diodes in circuits Diode need a turn on pd. Minimum pd for diode to turn on About 0.6V (forward pd or forward bias) Infinite resistance in reverse bias or below 0.6V forward bias In any working circuit the diode has 0.6V across it 0.6V 1.5V 0.9V I=0.9V/1.00Ω=0.9A

example P R Q

Example 2 cells P and Q in parallel across resistor R εP= 2.0V, rP=1.5Ω εQ= 1.5V, rQ=2.0Ω =? =? R = 4Ω P R Q

The potential divider – the theory A potential divider consists of two or more resistors in series with each other and with a source of fixed pd. The potential difference of the source is divided between the components in the circuit. A potential divider can be used to: supply a pd which is fixed at any value between 0V and the source pd Supply a variable pd between 0V and the source pd Supply a pd that varies with temperature or pressure or light intensity (using a thermistor, LDR etc)

To supply a fixed pd Two resistors in parallel R1, R2 Fixed pd source Vin I= Vin/(R1 + R2) V1=I R1 = Vin R1 /(R1 + R2) V2=I R2 = Vin R2 /(R1 + R2) V1/V2 = R1/R2 Ie the ratio of the pds across each resistance is equal to the ratio of the two resistances

Implementations of potential dividers http://www.furryelephant.com/player.php?subject=physics&jumpTo=ee/9D5s1

Uses of potential dividers A simple audio volume control to change the loudness of the sound from a loudspeaker. The audio signal pd is supplied to the potential divider in place of a cell or battery. The output variable is the pd across the loudspeaker To vary the brightness of a light bulb between zero and normal brightness. In contrast between using a variable resistor in series, the use of the potential divider enables the current to go from max to zero. With a variable resistor there would still be a current through the bulb when the resistance is at a maximum. Note there is a maximum current through dimmer switches so limit the power of the bulb! Now with AC they turn off for part of the cycle using semiconductors

Sensor circuits

Usually used with a transistor!

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