Series and Parallel Circuits

Complete Electrical Circuits

What two conservation laws are most important when analysing electrical circuits?

Conservation of charge and conservation of energy.

What does conservation of charge mean in a circuit?

The total amount of charge in the circuit cannot increase or decrease.

How must an ammeter be connected?

In series with the component whose current it is measuring.

Why is an ammeter connected in series?

Because current measures the flow of charge through a component, so the same charge must pass through the ammeter.

What is the rule for current in a series circuit?

The current is the same at all points in the series circuit.

Why is current the same throughout a series circuit?

There are no junctions for the charge to split at.

What happens to current at a junction?

It splits between the available branches.

What is the current rule at a junction?

The total current entering a junction equals the total current leaving it.

Write the current rule for two parallel branches.

I_total = I₁ + I₂.

Why must currents recombine after parallel branches?

To conserve charge.

How does resistance affect the current in different parallel branches?

A branch with a higher resistance carries a smaller current.

How must a voltmeter be connected?

In parallel across the component whose potential difference it is measuring.

Why is a voltmeter connected in parallel?

Because potential difference measures the energy transferred per unit charge between two points.

What is the rule for emf values in series?

The total emf is the algebraic sum of the individual emfs.

What happens if cells in series are connected in the same direction?

Their emfs add together.

What happens if cells in series are connected in opposite directions?

Their emfs oppose each other, so one is subtracted from the other.

What is the rule for potential differences in series?

The total potential difference is the sum of the individual potential differences.

Write the voltage rule for components in series.

V_total = V₁ + V₂ + ...

Why do potential differences add in a series circuit?

Because of conservation of energy: the total energy transferred per unit charge must equal the energy supplied per unit charge.

What is the rule for voltage across parallel branches?

The potential difference is the same across every parallel branch.

Why is the potential difference the same across parallel branches?

Each branch is connected between the same two points in the circuit.

What does Ohm's law equation state?

V = IR.

How can resistance be calculated from voltage and current?

R = V/I.

What is the rule for resistors connected in series?

Their resistances add directly.

Write the equation for total resistance in series.

R_total = R₁ + R₂ + R₃ + ...

Why do resistances add in series?

The current is the same through each resistor while the total potential difference is the sum of the individual potential differences.

Derive the series resistance equation using Ohm's law.

V_total = V₁ + V₂ + V₃, so IR_total = IR₁ + IR₂ + IR₃, therefore R_total = R₁ + R₂ + R₃.

What is the equation for resistors connected in parallel?

1/R_total = 1/R₁ + 1/R₂ + 1/R₃ + ...

Why is the total resistance of parallel resistors lower than the individual resistances?

Adding more parallel paths gives charge more routes through the circuit, increasing the total current for the same voltage.

How does the total resistance of a parallel combination compare with the smallest individual resistance?

It is always smaller than the smallest individual resistance.

What is the current relationship for resistors in parallel?

I_total = I₁ + I₂ + I₃ + ...

What is the voltage relationship for resistors in parallel?

V₁ = V₂ = V₃ = V_total.

Derive the parallel resistance equation using Ohm's law.

I_total = I₁ + I₂ + I₃ and I = V/R, so V/R_total = V/R₁ + V/R₂ + V/R₃, giving 1/R_total = 1/R₁ + 1/R₂ + 1/R₃.

What is the total resistance of two identical resistors R connected in parallel?

R/2.

What is the total resistance of three identical resistors R connected in parallel?

R/3.

If two 100 kΩ resistors are connected in parallel, what is their combined resistance?

50 kΩ.

How do you deal with a circuit containing both series and parallel resistors?

Calculate the equivalent resistance of one group at a time, then combine those equivalent resistances using the correct series or parallel rule.

What should you calculate first in a mixed circuit?

Usually identify a simple parallel or series group and find its equivalent resistance first.

Do ideal ammeters significantly affect the resistance of a circuit?

No. An ideal ammeter has negligible resistance.

Do ideal voltmeters significantly affect the resistance of a circuit?

No. An ideal voltmeter has a very large resistance and draws negligible current.

What happens to the total resistance when another resistor is added in series?

The total resistance increases.

What happens to the total resistance when another resistor is added in parallel?

The total resistance decreases.

What happens to current in a series circuit if the total resistance increases while the supply voltage stays constant?

The current decreases.

What happens to total current if another parallel branch is added while the supply voltage stays constant?

The total current increases because the total resistance decreases.

If a 10 Ω resistor and a 20 Ω resistor are connected in series, what is the total resistance?

30 Ω.

If 0.2 A flows through a 10 Ω resistor, what is the potential difference across it?

V = IR = 0.2 × 10 = 2 V.

If 0.2 A flows through a 20 Ω resistor, what is the potential difference across it?

V = IR = 0.2 × 20 = 4 V.

If resistors in series have potential differences of 2 V and 4 V, what is the total potential difference?

6 V.

If a 6 V supply is connected across parallel branches, what is the potential difference across each branch?

6 V.

If 3 A reaches a junction and 1 A goes through one branch, what current must flow through the other branch?

2 A.

If a 12 V supply is across a 100 Ω resistor, what current flows?

I = V/R = 12/100 = 0.12 A.

If a 12 V supply is across a 50 Ω resistor, what current flows?

I = V/R = 12/50 = 0.24 A.

If currents of 0.12 A and 0.24 A flow in two parallel branches, what is the total current?

0.36 A.

If three parallel resistors are 16 Ω, 24 Ω and 48 Ω, what is the total resistance?

1/R = 1/16 + 1/24 + 1/48 = 6/48 = 1/8, so R = 8 Ω.

What is the difference between a series circuit and a parallel circuit?

A series circuit has a single path for current, whereas a parallel circuit has junctions and multiple paths.

What happens if one component breaks in a simple series circuit?

The circuit is broken and current stops everywhere.

What happens if one branch breaks in a parallel circuit?

Other complete branches can still carry current.

Why are household circuits generally connected in parallel?

So each appliance receives the full supply voltage and can operate independently.

How can conservation of charge be seen at a circuit junction?

The sum of currents entering the junction equals the sum of currents leaving it.

How can conservation of energy be seen around a complete circuit loop?

The total emf supplied equals the sum of the potential differences across the components.

State Kirchhoff's first law.

The total current entering a junction equals the total current leaving the junction.

State Kirchhoff's second law.

Around a closed loop, the sum of the emfs equals the sum of the potential differences.

Which conservation law leads to Kirchhoff's first law?

Conservation of charge.

Which conservation law leads to Kirchhoff's second law?

Conservation of energy.

Why is current not 'used up' by a component?

Current is the rate of flow of charge, and charge is conserved.

What is transferred or dissipated by components instead of charge being used up?

Energy.

Why can the current be different in separate parallel branches?

The current divides according to the resistance of each branch.

Which parallel branch carries more current: a high-resistance branch or a low-resistance branch?

The low-resistance branch.

For two parallel branches with the same voltage, how are current and resistance related?

Current is inversely proportional to resistance.

If two parallel resistors have resistances of 100 Ω and 50 Ω, which carries twice the current?

The 50 Ω resistor.

What quantity stays the same through components connected in series?

Current.

What quantity is shared between components connected in series?

Potential difference.

What quantity stays the same across components connected in parallel?

Potential difference.

What quantity splits between branches connected in parallel?

Current.

What happens to the total emf of two 1.5 V cells connected in series in the same direction?

It becomes 3.0 V.

What happens to the total emf of two identical 1.5 V cells connected in opposite directions?

They cancel, giving a net emf of 0 V.

What is meant by equivalent resistance?

A single resistance that would have the same effect on the circuit as a combination of resistors.