# ELECTRICAL CIRCUITS

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• Created by: CPev3
• Created on: 27-05-20 19:09

## Kirchhoff's laws

ΣIinΣIout

Sum of currents into a point = sum of currents out of that point

Number of charge carriers entering = number of charge carriers leaving

Based on the law of conservation of charge

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ΣE = ΣV around a closed loop

Sum of electromotive forces = sum of potential differences

Total energy transferred to charges = total energy transferred from charges

Based on the law of conservation of energy

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## Series circuits

• One path for current
• Current the same in every position
• Electromotive force shared between components
• ↑ resistance = ↓ potential difference
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## Parallel circuits

• Multiple paths for current
• ↑ resistance of branch = ↓ current
• Potential difference across each branch = electromotive force
• If changes are made to one branch, the others are not affected
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## Resistors in series

↑ number of resistors

= length of the path taken by charges

=  resistance

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1. Kirchhoff's 2nd law: V = V1 + V2 + ...

2. V = IR: IR = IR1 + IR2 + ...

3. Kirchhoff's 1st law: R = R1 + R2 + ...

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## Resistors in parallel

↑ number of resistors

number of paths taken by charges

= ↑ cross-sectional area

↓ resistance

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1. Kirchhoff's 1st law: I = I1 + I2 + ...

2. Kirchhoff's 2nd law: I/V = I1/V + I2/V

3. V = IR: 1/R = 1/R1 + 1/R2 + ...

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## Internal resistance

Work done by charges as they move through power source

Some energy transferred into heat

Not all energy transferred to charges is available to circuit

Terminal potential difference < electromotive force

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## Electromotive force equation 1

Electromotive force = terminal potential difference + lost volts

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↑ current

↑ charges travelling through the cell per second

↑ work done by charges

↑ lost volts

↓ terminal potential difference

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Lost volts = current x internal resistance

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## Electromotive force equation 2

ε = V + lost volts

ε = V + Ir

ε = IR + Ir

ε = I(R + r)

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## V-I graph

V = -rI + ε

• Y-intercept = ε

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2 x ε and same r

• 2 x y-intercept

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Same ε and 1/2 r

• Same y-intercept
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## Potential divider

Connected to a fixed input

Divides the potential difference across multiple components to produce a specific output

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## Potential divider equations

V1 / V2 = R1 / R2

Vout = (R / (R1 + R2)) x Vin

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## Producing a varying Vout

Replace one of the fixed resistors with a

• Variable resistor
• ↑ R = ↑ Vout
• LDR
• ↑ light intensity = ↓ R = ↓ Vout
• Thermistor
• ↑ temperture = ↓ R = ↓ Vout
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## Potentiometer

• Variable resistor
• Three terminals + sliding contact
• Produces a variable Vout

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• Contact moved towards A: ↑ Vout
• Contact at A: Vout = Vin
• Contact moved towards B: ↓ Vout
• Contact at A: zero Vout
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