5.7 - parallel circuits

Dr Pusey

www.puseyscience.com

Syllabus PointsCircuit analysis and design involve calculation of

the potential difference across, the current in, and the power supplied to, components in series, parallel, and series/parallel circuits

This includes applying the relationships for parallel components:

𝑉 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡𝐼𝑡 = 𝐼1 + 𝐼2 +⋯𝐼𝑛1

𝑅𝑡=

1

𝑅1+

1

𝑅2+⋯

1

𝑅𝑛

Learning GoalsBe able to use the equations below to determine

potential difference, current, power and resistance in parallel circuits

𝑉 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡𝐼𝑡 = 𝐼1 + 𝐼2 +⋯𝐼𝑛1

𝑅𝑡=

1

𝑅1+

1

𝑅2+⋯

1

𝑅𝑛Apply your knowledge of electrical circuits to everyday

situations to explain how they work

Compare and contrast the properties of series and parallel circuits

Parallel circuits

Each component is connected directly to the voltage source

At least two different pathways for current to travel

Current in a Parallel circuit Current splits along the different pathways (but not

equally)

Charge is conserved – so current going into a junction = current coming out of the junction

In reality, if the power source can’t cope, the total current will be limited.

𝐼𝑡 = 𝐼1 + 𝐼2 +⋯𝐼𝑛

Resistance in parallel circuits Amount of current travelling through

each pathway in a parallel circuit depends on the resistance of the pathway

The equivalent resistance (total resistance) of a parallel circuit is the amount of resistance that a ‘single’ resistor would need in order to equal the overall effect.

As more resistors are added in parallel, the overall resistance decreases!

Research the water pipe analogy for help understanding this concept.

1

𝑅𝑇=

1

𝑅1+

1

𝑅2+. . . .

Potential difference in a parallel circuit

The same voltage/potential difference is applied to each pathway of a parallel circuit, without exception.

Since resistance is different for different pathways (previous slide), the current will change accordingly.

Example 1Two car headlights have the same resistance R.

a) Which configuration produces more light (series or parallel)? [Find the total resistance in each case, in terms of R]

b) Which way do you think the headlights of a car are wired?

Example 1

Two car headlights have the same resistance R.

a) Which configuration produces more light (series or parallel)? [Find the total resistance in each case, in terms of R] Parallel

b) Which way do you think the headlights of a car are wired? Parallel

Example 2For the circuit pictured below, R1= 10 Ω, R2= 25 Ω and R3= 10 Ω, calculate the:

a) Total/equivalent resistance

b) Current between points 27

c) Current between points 36

d) Current between points 45

Example 2For the circuit pictured below, R1= 10 Ω, R2= 25 Ω and R3= 10 Ω, calculate the:

a) Total/equivalent resistance

Example 2For the circuit pictured below, R1= 10 Ω, R2= 25 Ω and R3= 10 Ω, calculate the:

b) Current between points 27

Example 2For the circuit pictured below, R1= 10 Ω, R2= 25 Ω and R3= 10 Ω, calculate the:

c) Current between points 36

Example 2For the circuit pictured below, R1= 10 Ω, R2= 25 Ω and R3= 10 Ω, calculate the:

d) Current between points 45

Example 3 Fill in the blanks on the following circuit diagram

Example 3 Fill in the blanks on the following circuit diagram

Example 4 Suppose you have a 680 Ω resistor, a 940 Ω resistor,

and a 1.2 kΩ resistor. What is:

a) The maximum resistance

b) The minimum resistance

You can obtain by combining these resistors?

Example 4 Suppose you have a 680 Ω resistor, a 940 Ω resistor,

and a 1.2 kΩ resistor. What is:

a) The maximum resistance

b) The minimum resistance

You can obtain by combining these resistors?

Context – Lights at home

Why are your lights and other appliances at home wired in parallel?

Parallel Circuit – sum up Current = different in different branches, but total

amount is conserved (current going into a branch = current coming out of branch)

Resistance = lower than individual resistance of components

Potential difference is the same on all branches

1

𝑅𝑇=

1

𝑅1+

1

𝑅2+. . . .

ResourcesAV

Khan Academy - Circuits (part 1) (11:40)

Khan Academy - Circuits (part 2) (11:08)

Khan Academy - Circuits (part 3) (12:21)

Khan Academy - Circuits (part 4) (7:07)

Simulation

PhET – DC circuit construction kit