Model Answers - electric circuits

Question 1

Define potential difference

Answer 1

potential difference is the energy transferred (or work done) between two points in a circuit per unit charge (V = W/Q)

Question 2

Define EMF

Answer 2

emf is the work done per unit charge by the power supply or cell, converting energy into electrical potential energy of the charges

Question 3

Define current

Answer 3

the rate of flow of charge (I = ∆Q/∆t)

Question 4

Derive the equation linking current with the number of electrons N flowing past a point in a time ∆t with the current

Answer 4

The charge flow ∆Q = Ne where e is the magnitude of the charge on each electron, e=1.6x10-19 C
I = Ne / ∆t

Question 5

Explain how to calculate the number of electrons in a certain amount of charge

Answer 5

Number of electrons = total charge / charge on one electron
o N = Q/ 1.6 x10 ^-19

Question 6

Define resistance

Answer 6

the ratio of pd to current (R=V/I)

Question 7

Derive the formula for the ratio of currents down parallel branches of a circuit

Answer 7

The pd across each branch is the same V1 = V 2
o V = IR so
o I1R1 = I2R2
o So I1 / I2 = R2 / R1
o Or, the ratio of the currents is the reciprocal of the ratio of the resistances
o Eg. If resistor 1 is 100 times greater in resistance than resistor 2, it will receive 100 times less current than resistor 1

Question 8

Derive the formula for resistors in series

Answer 8

Vtotal = V1 + V2 + V3 (due to energy conservation)
o V= IR so
o ItotalRtotal = I1R1 + I2R2 + I3R3
o Itotal = I1 = I2 = I3 = I (charge conservation)
o lRtotal = IR1 + IR2 + IR3
o Rtotal = R1 + R2 + R3

Question 9

Derive the formula for resistors in parallel

Answer 9

o Itotal = I1 + I2 + I3 (due to charge conservation)
o I= V/R so
o Vtotal / Rtotal = V1/R1 + V2/R2 + V3/R3
o Vtotal = V1 = V2 = V3 = V (due to energy conservation)
o V/ Rtotal = V/R1 + V/R2 + V/R3
o 1/Rtotal = 1/R1 + 1/R2 + 1/R3

Question 10

Answer 10

Question 11

State Kirchoff’s potential difference law

Answer 11

The sum of the potential difference is equal to the sum of the emfs around a closed loop within a circuit
- this is due to conservation of energy

Question 12

State Kirchoff’s current law

Answer 12

The sum of the currents into a junction is equal to the sum of the currents out of the junction
o this is due to conservation of charge

Question 13

Answer 13

To determine the resistance of the resistor, the student would use R = V/I where V is the pd across the resistor and I is the current through the resistor
o An ideal ammeter has zero resistance
o If the ammeter had non-zero resistance, then there would be potential difference across it
o Therefore the potential difference measured by the voltmeter would be the sum of the pd across the ammeter and the pd across the resistor. This would be problematic as the resistance calculation requires only the pd across the resistor (the voltmeter position would have to change to be only around the resistor).
o An ideal voltmeter has infinite resistance
o If the voltmeter had non-infinite resistance then it would draw some current and reduce the total resistance of the circuit, increasing the overall current.
o However, this would not affect the resistance determination, as the ammeter would still be measuring the genuine current through the resistor
o So student B is correct

Question 14

Answer 14

To determine the resistance of the resistor, the student would use R = V/I where V is the pd across the resistor and I is the current through the resistor
o An ideal voltmeter has infinite resistance
o If the voltmeter had non-infinite resistance then it would draw some current (and increase the total current in the circuit as the total resistance of the circuit would decrease)
o This would mean that the ammeter reading would give the sum of the current through the resistor and the current through the voltmeter
o This would mean the resistance calculation would not be possible as this should only use the current through the resistor, which is not measured here
o If the ammeter had non-zero resistance, then the total resistance of the circuit would increase and there would be potential difference across it
o Neither of those consequences are problematic though, as the voltmeter still only reads the pd across the resistor, and the current reading is still the same current passing through the resistor
o So the ammeter can have a non-zero resistance and student B is correct.

Question 15

Define lost volts

Answer 15

The energy per unit charge transferred to the internal resistance of a cell (Ir)

Question 16

Define terminal potential difference

Answer 16

V = EMF – Ir where r is the internal resistance of the cell and I is the current through the cell

Question 17

Explain why connecting an ideal voltmeter directly around a cell allows us to measure the EMF directly

Answer 17

The ideal voltmeter has infinite resistance
o So the current is approximately zero
o So as terminal pd = EMF – lost volts,
o V = E – Ir
o The lost volts is zero
o And terminal pd is equal to EMF

Question 18

Answer 18

Student A is correct
o Because the wires we assume to have zero resistance
o Therefore there is no potential difference dropped across the wires
o So, as the sum of the EMF is equal to the sum of potential difference drops
o Both voltmeters read the terminal potential difference, V = EMF- Ir

Question 19

Explain what happens to the reading on the voltmeter as the resistance of the variable resistor is decreased

Answer 19

The voltmeter reads the terminal potential difference, V
o V = EMF – Ir
o As the resistance of the variable resistor is decreased, the total resistance in the circuit decreases
o Meaning the current, I = EMF / (Rtotal) will increase
o So the lost volts, Ir will increase
o And as the EMF is fixed
o Terminal pd will decrease

Question 20

Explain why a battery will get hot when the current passing through it is high

Answer 20

If the current is high, the lost volts, Ir will be high
o So there will be a large amount of energy per unit charge transferred to the internal resistance of the cell
o This energy is transferred to the resistor ions
o Causing them to vibrate with higher amplitudes, increasing the temperature

Question 21

Draw the circuit diagram required to determine the emf and internal resistance of a cell:
 

Answer 21

Question 22

Describe how to perform an experiment to determine the EMF and internal resistance of a cell:

Answer 22

Question 23

Answer 23

The x intercept is when the terminal potential difference is zero
o This means that all of the EMF is being transferred to the internal resistance of the cell as ‘lost volts’
o no energy is being transferred to the load resistance and the current cannot continue to increase
o the y-intercept is when the EMF is equal to the terminal potential difference
o this is when the current is zero and therefore no energy is being transferred to the internal resistor
o lost volts, Ir is zero

Question 24

Answer 24

When the extra light bulb is connected in parallel, the total resistance of the circuit decreases
o This means the total current in the circuit increases, as Itotal = EMF / Rtotal and the EMF is fixed
o So the lost volts, Ir, increases
o This means the terminal pd across AB decreases, as Vterminal = EMF - Ir

Question 25

What can we say about the brightness of each light bulb after an extra light bulb is connected to the circuit (assuming the brightness of the bulb increases with the energy transferred)?

Answer 25

The power across AB is given by P=V2/R where V is the pd across AB and R is the resistance of the bulb between A and B
o As the terminal pd decreases as extra bulbs are added (because lost volts increases due to the increase in current caused by the decrease in total resistance), the power across AB will decrease
o And therefore the brightness will decrease as extra bulbs are added