EI · 8 cards

Parallel Circuits flashcards

8 cards with the formulas, rules and traps from this lesson. Answer in your head, then flip to check.

Term · 1/8
What is the defining test for two components being in parallel?
Both ends share the same two nodes: one end of each on node A, the other end of each on node B. Drawing position and equal values do not matter.
Rule · 2/8
In a parallel circuit, what is shared and what divides?
Every branch gets the same full voltage, and the current divides: $I_{T} = I_{1} + I_{2} + I_{3} + \dots$ . Each branch current is $I_{n} = V / R_{n}$ .
Formula · 3/8
Reciprocal rule for equivalent resistance of parallel resistors?
$\frac{1}{R _{e q}} = \frac{1}{R _{1}} + \frac{1}{R _{2}} + \frac{1}{R _{3}} + \dots$ , then flip the sum. Forgetting the final flip leaves an answer in siemens, not ohms.
Formula · 4/8
Product-over-sum shortcut for exactly two parallel resistors?
$R_{e q} = \frac{R _{1} R _{2}}{R _{1} + R _{2}}$ . Example: 20 $Ω$ and 30 $Ω$ give 600/50 = 12 $Ω$ . For n equal resistors use $R / n$ .
Fact · 5/8
How does the equivalent resistance of a parallel group compare with its branches?
It is always smaller than the smallest branch. Adding any branch lowers it and raises total current; removing or opening a branch raises it.
Formula · 6/8
How do two parallel branch currents split from a known total?
Inversely to resistance: $I_{1} = I_{T} \times \frac{R _{2}}{R _{1} + R _{2}}$ . Example: 2 $Ω$ and 8 $Ω$ sharing 10 A carry 8 A and 2 A. The smallest resistor carries the most current.
Fact · 7/8
In parallel, which resistor dissipates the most power, and why?
The smallest one. With the same voltage on every branch, $P_{n} = V^{2} / R_{n}$ , so power is inversely proportional to resistance. Branch powers add to $P_{T} = V I_{T}$ .
Common trap · 8/8
What happens to other branches when one parallel branch opens, versus a short across the rails?
An open branch only loses its own current; with an ideal source the others keep the same voltage and current. A short across the rails shorts every branch and the source, drawing very large current.

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