4.3 Electrical Circuits

module 4

State Kirchhoff's second law.

Around a closed loop:

total e.m.f. = total p.d.

Physics link:

conservation of energy

When do you use Kirchhoff's second law?

Use around a complete loop.

Use for:

series circuits

multiple cells

internal resistance

potential dividers

Series circuit rules.

Current is same everywhere.

P.d. is shared.

Total resistance:

Rtotal = R1 + R2 + …

Parallel circuit rules.

P.d. is same across each branch.

Current splits.

Total current:

Itotal = I1 + I2 + …

Resistance in parallel.

1/Rtotal = 1/R1 + 1/R2 + …

For two resistors:

Rtotal = R1R2 / (R1 + R2)

How do you handle circuits with multiple e.m.f. sources?

Choose loop direction.

Cell helping loop direction:

add e.m.f.

Cell opposing loop direction:

subtract e.m.f.

Then use Kirchhoff's second law.

Define internal resistance.

Resistance inside a source of e.m.f.

It causes energy loss inside the source.

Define terminal p.d.

P.d. across the terminals of a source.

This is the p.d. supplied to the external circuit.

Define lost volts.

P.d. across internal resistance.

lost volts = Ir

Link e.m.f., terminal p.d. and lost volts.

epsilon = V + Ir

V = terminal p.d.

Ir = lost volts

When do you use epsilon = I(R + r)?

Use for a source with internal resistance and external resistance.

epsilon = I(R + r)

R = external resistance

r = internal resistance

Why does terminal p.d. fall as current increases?

Lost volts increase.

lost volts = Ir

V = epsilon - Ir

So higher I gives lower V.

When is terminal p.d. equal to e.m.f.?

When current is zero.

I = 0

lost volts = 0

V = epsilon

PAG: How do you determine internal resistance?

Set up:

cell

variable resistor

ammeter in series

voltmeter across cell

Vary resistance.

Record V and I.

Plot V against I.

PAG: Internal resistance graph.

Equation:

V = epsilon - Ir

Plot:

V against I

y-intercept = epsilon

gradient = -r

internal resistance = -gradient

Define potential divider.

Circuit that gives output p.d. as a fraction of input p.d.

Uses resistors in series.

State potential divider equation.

Vout = Vin x Rout / Rtotal

For two resistors:

Vout = Vin x R2 / (R1 + R2)

where Vout is across R2.

How do you choose Rout?

Rout is the resistance across the output terminals.

Use:

Vout = Vin x Rout / Rtotal

What happens if Rout increases?

Vout increases.

Because:

Vout = Vin x Rout / Rtotal

How does an LDR work in a potential divider?

Bright light:

LDR resistance decreases

Dark:

LDR resistance increases

Vout depends on where the LDR is placed.

How does a thermistor work in a potential divider?

Temperature increases.

Thermistor resistance decreases.

Vout depends on whether output is across thermistor or fixed resistor.

PAG: How do you investigate a potential divider?

Set up two resistors in series.

Connect voltmeter across output resistor.

Use LDR or thermistor as one resistor.

Change light intensity or temperature.

Record Vout.

PAG: Controls for potential divider.

Keep Vin constant.

Keep fixed resistor constant.

Measure Vout across same component.

For LDR:

control distance from lamp.

For thermistor:

allow temperature to stabilise.

How do you design a light-sensing circuit?

Use LDR in potential divider.

Bright light:

LDR resistance decreases

Dark:

LDR resistance increases

Choose output position depending on whether Vout should rise in light or dark.

How do you design a temperature-sensing circuit?

Use thermistor in potential divider.

Temperature rises:

thermistor resistance decreases

Choose output position depending on whether Vout should rise or fall with temperatu