One loop or several paths?

Series components carry the same current and their voltage drops add. Parallel branches have the same potential difference and their currents add. These statements express charge and energy conservation, respectively.

Series resistances add. Parallel conductances add, so adding a branch lowers total resistance. Power P = VI is the rate of energy transfer; for a resistor it is also I²R or $V^{2}$ /R. A kilowatt-hour is energy, not power.

INTERACTIVE MODEL

Add a parallel branch

Second resistance / Ω10

READ THE GRAPH

Explore the relationship

A fixed 10 Ω branch in parallel with the adjustable branch. Total current is the sum of branch currents.

Total current / A

Tap or focus a plotted point to read its values.

View plotted data as a table

Explore the relationship
Series	Supply voltage / V	Total current / A
Total current / A	0	0
Total current / A	0.2	0.04
Total current / A	0.4	0.08
Total current / A	0.6	0.12
Total current / A	0.8	0.16
Total current / A	1	0.2
Total current / A	1.2	0.24
Total current / A	1.4	0.28
Total current / A	1.6	0.32
Total current / A	1.8	0.36
Total current / A	2	0.4
Total current / A	2.2	0.44
Total current / A	2.4	0.48
Total current / A	2.6	0.52
Total current / A	2.8	0.56
Total current / A	3	0.6
Total current / A	3.2	0.64
Total current / A	3.4	0.68
Total current / A	3.6	0.72
Total current / A	3.8	0.76
Total current / A	4	0.8
Total current / A	4.2	0.84
Total current / A	4.4	0.88
Total current / A	4.6	0.92
Total current / A	4.8	0.96
Total current / A	5	1
Total current / A	5.2	1.04
Total current / A	5.4	1.08
Total current / A	5.6	1.12
Total current / A	5.8	1.16
Total current / A	6	1.2
Total current / A	6.2	1.24
Total current / A	6.4	1.28
Total current / A	6.6	1.32
Total current / A	6.8	1.36
Total current / A	7	1.4
Total current / A	7.2	1.44
Total current / A	7.4	1.48
Total current / A	7.6	1.52
Total current / A	7.8	1.56
Total current / A	8	1.6
Total current / A	8.2	1.64
Total current / A	8.4	1.68
Total current / A	8.6	1.72
Total current / A	8.8	1.76
Total current / A	9	1.8
Total current / A	9.2	1.84
Total current / A	9.4	1.88
Total current / A	9.6	1.92
Total current / A	9.8	1.96
Total current / A	10	2
Total current / A	10.2	2.04
Total current / A	10.4	2.08
Total current / A	10.6	2.12
Total current / A	10.8	2.16
Total current / A	11	2.2
Total current / A	11.2	2.24
Total current / A	11.4	2.28
Total current / A	11.6	2.32
Total current / A	11.8	2.36
Total current / A	12	2.4

Probe along the horizontal axis0Total current / A: 0

Explore: Change the second parallel resistance and compare the total supply current.

R_s=R_1+R_2\qquad\frac1{R_p}=\frac1{R_1}+\frac1{R_2}\qquad P=VI

WORKED EXAMPLE

Connect 6 Ω and 3 Ω in parallel across an ideal 12 V supply.

Branch currents are 2 A and 4 A; total is 6 A.
Equivalent resistance = $\frac{12}{6}$ = 2 Ω.

Assumed knowledge

Ohm’s law.

Learning checkpoints & source

YOUR LEARNING CHECKPOINT

Apply series and parallel circuit rules.
Calculate electrical power and energy.

QCAA Physics · Unit 1 · Electrical circuits ↗

READY TO TRY IT?

One loop or several paths?

Add a parallel branch

Explore the relationship

Connect 6 Ω and 3 Ω in parallel across an ideal 12 V supply.

Put the idea to work.