CIRCUITS AND ELECTRICITY

Circuits

Circuits

Cells in series

If cells are connected up in series with one another and all face the same direction then the total potential difference being supplied to the circuit can be calculated by summing up each of the potential differences. For example:

Vtotal = V1 + V2 + V3

Identical cells in parallel

If there are identical cells in parallel with one another then the total potential difference being supplied to the circuit is equal to only one of the cells. For example:

Vtotal = V1 = V2 = V3

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Resistors in series

As with cells in series, if resistors are connected up in series with one another then the total potential difference being supplied to the circuit can be calculated by summing up each of the potential differences. For example:

Rtotal = R1 + R2 + R3

Resistors in parallel

If there are resistors parallel with one another then you must use the equation below to work out the total resistance:

1/R = 1/R1 + 1/R2 + 1/R3

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Current in series and parallel circuits

For currents in series and parallel circuits:

  • Conservation of charge: ‘the total charge flowing into a junction of wires must equal the total charge flowing out of the junction.’
  • Kirchoff’s first law: ‘the sum of the currents flowing into a junction of wires must equal the sum of the currents flowing away from the junction of wires.’

Therefore:

I1 = I2 + I3 + I4

Current in series circuits

If an ammeter is placed into a series circuit, the current measurement will be the same wherever it is connected.

Current in parallel circuits

The total current flowing from a cell to the branches within a circuit must equal the current which is flowing through all the components in the branches of the circuit once they are summed up.

If the components possess different resistances then the current flowing through each component could be different. However, once they have been summed up, the total must be equal to the amount of current which is leaving the cell.

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Potential difference in series and parallel circuits

For potential difference in series and parallel circuits you must consider Kirchoff’s second law: ‘the sum of the emf’s in any closed loop in a circuit must be equal to the sum of the potential differences in the closed loop in the circuit.’

Potential difference in a series circuit

The total potential difference being supplied by the cell is split up between the different components. Therefore, if each component has the same resistance then they will all have an equal amount of potential difference flowing across them.

If the resistances are not equal then they could have different potential difference flowing across them. However, when summed up, the resistances must be equal to the potential difference being supplied by the cell.

Potential difference in parallel circuits

In this case, the potential difference being supplied by the cell is equal to the potential difference across each component within the parallel circuit.

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Energy and Power in Circuits

There are three formulae that you should be aware of in connection with energy and power in circuits.

Energy (E) is measured in joules (J):

E = VIt

In which:

  • E = energy in joules (J)
  • V = potential difference in volts (V)
  • I = current in amperes (A)
  • t = time in seconds (s)

Power (P) is measured in watts (W). Power is described as the rate at which energy is transferred. One watt is equivalent to one joule per second: 1W = 1Js-1.

P = VI

In which:

  • P = power in watts (W)
  • V = potential difference in volts (V)
  • I = current in amperes (A)

P = I2R

In which:

  • P = power in watts (W)
  • I = current in amperes (A)
  • R = resistance in ohms (?)