Notes: Series and parallel

Series:

A single wire (with no junctions) connects one device to the other.
The same current MUST pass through both.

Parallel:

A wire (with or without junctions) connects one device to the other)
AND a second wire connects the opposite ends of the same two devices.
Both must have the same potential difference.

Example: Circuit reduction

Left

Which devices are in series? (ℰ and R₁)
↑ single wire (on left) connects the two
Which devices are in parallel? (R₂ and R₃)
↑ branched wire connects left, and a second branched wire connects right

Right

Which devices are in series? NONE
Which devices are in parallel? (R₁ ∥ R₂, R₃ ∥ R₄)
Note: R₁ is not parallel to R₃ or R₄

Problem: bulb brightness

Question

6 identical light bulbs (resistance R), connected into circuits with two identical batteries.
Rank bulbs by brightness (least to greatest)
Which circuit consumes more power?

Answer

Currents: B = 0, E = F = ℰ / (3R), A = C = ℰ / (2R), D = ℰ / (1.5R)
Remember, power consumed = power supplied by the battery = ℰ × (current through battery)
Left power = ℰ² / (2R)
Right power = ℰ² / (1.5R)

Numbers

Let ℰ = 2.0V, R = 1.0Ω
I_L = 1.0A, P_batt = 2W, P_A = P_B = 1W
I_R = 1.3A, P_batt = 2.7W, P_D = 1.8W, P_E = P_F = 0.44W