5: Electric Current 5.2 Electric Circuits

Resistor Combinations Experiment: Resistance in series and parallel circuits. Use a voltmeter and ammeter or Ohmmeter to determine the resistance of a range of components. Then connect them in series or in parallel pairs and investigate the overall resistance.

IRe = IR1 + IR2 (Re = total equivalent resistance) Resistors in Series Current (I) is equal in both The supply voltage is shared across the resistors R1 R2 Vs = V1 + V2 IRe = IR1 + IR2 (Re = total equivalent resistance) but I cancels out giving… Re = R1 + R2 for resistors in series

for resistors in parallel I = I1 + I2 but... I = so... V cancels giving... I2 R2 R1 I I1 Total current (I) is shared between the two resistors The voltage across each is equal (V) VR VRe VR1 VR2 = + 1 Re 1 R1 1 R2 = + for resistors in parallel

E.g.2.Put these in increasing order of magnitude E.g. Calculate the equivalent resistance of these resistor combinations: E.g.2.Put these in increasing order of magnitude 750Ω 1200Ω 1200Ω 120Ω 360Ω

The Potential Divider Circuit We know that for resistors in series, the supply voltage is shared between the individual resistors. Demo: Measure V and the voltages across the two resistors. Predict how the voltages would change if you swapped the 1kΩ resistor for a 4kΩ resistor? 1 kΩ 2 kΩ V V1 V2 Conclusion: The ratio of the resistances is the same as the ratio of the voltages Q. Using V=IR, explain why the bigger resistor will always take a larger voltage.

A circuit like this is known as a potential divider because it divides up the total p.d. supplied by the cell. The voltage across one of the resistors can then be used as an output supply to an external device or circuit. E.g. Assuming voltage V is shared across the two resistors… V = I R  V = I (R1 + R2)  I = V R1 + R2 but… Vout = IR2 so… Vout = V R2 R1 R2 V I Vout (where R = equivalent resistance) This is called the potential divider formula

E.g. Determine the total resistance and hence the current in the circuit. Determine the output voltage in the circuit. If a bulb was connected across the output, how would this affect the output voltage? 6Ω 9Ω V I Vout 12V R = 15Ω so… I = 0.8A V = 7.2V A parallel section would be created, thus reducing the total resistance between the output terminals and thus also reducing the output voltage. Extension: If the bulb has resistance 18Ω, determine the new Vout?

( Demo / Experiment - LDR, 2.2kΩ, 2 cells, voltmeter )

Sensors and potential dividers 1. Strain gauge The diagram below shows part of an F1 car suspension. A strain gauge is stuck on the underside of strut X and wired into the circuit shown. Explain what a decrease in measured output voltage would indicate. R2 V I Vout Strain gauge X

2. Automatic light switch The electronic switch will turn on the lights (on another circuit) if the voltage rises above a certain fixed value. i. What happens to the LDR resistance when the light level falls? ii. So what happens to Vout? iii. What happens next? R1 V I Vout Electronic switch LDR

A potentiometer is a variable potential divider. The Potentiometer A potentiometer is a variable potential divider. R1 R2 V I Vout The slider can be moved to alter the ratio of R1 to R2 A B C Q. At which positions would the slider enable the bulb to i. be brightest? ii. be off (Vout= 0)?

EMF and Internal Resistance For components that put energy into a circuit, the p.d. across them is referred to as the Electro Motive Force (EMF). Therefore… However the voltage measured across the terminals of the cell (the terminal p.d.) is often less than the EMF. The EMF of a cell is the amount of work done by the cell per Coulomb of charge passing through the circuit.

Observations and Conclusion: Internal Resistance Demo / Experiment: V I Set up the circuit and measure the voltage across the cell. Add one, then two, then three bulbs in parallel. What happens to V? Observations and Conclusion: The terminal p.d. decreases as the resistance of the circuit decreases. This indicates that the cell must have resistance itself, taking a gradually larger share of the EMF (this is now like a potential divider circuit).

Internal Resistance All cells (and other sources of EMF) have an internal resistance, r (effectively in series). This is why cells heat up during use. r I R V Terminal voltage Lost voltage across r = Ir Thus… EMF = Ir + V but… V = IR so… EMF = I (r +R) EMF Experiment: Aim: Determine the internal resistance of a single cell.

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