Series, Parallel, and Mixed Resistor Circuits: Analysis and Power

All flashcards

How can you recognize resistors in series?

They are connected sequentially along a single path, so current has no alternate route around any resistor.

What is the equivalent-resistance rule for parallel resistors?

Add the reciprocals of the resistances; the reciprocal of that sum is the equivalent resistance.

How do voltage and current behave in parallel branches?

Each branch has the same voltage, while branch currents depend on resistance and add at a junction.

How can a mixed resistor circuit be simplified?

Replace a clearly identified series or parallel group with its equivalent resistance, then reassess the circuit.

How can resistor power be calculated?

$P = IV = I^2R = \frac{V^2}{R}$; choose the form that uses known values.

Quiz questions

1. Three resistors of $4\,\Omega$, $6\,\Omega$, and $10\,\Omega$ are connected in series. What is their equivalent resistance?Answer: $20\,\Omega$
2. Which connection defines resistors as parallel?Answer: Each resistor connects across the same two nodes.
3. Two parallel branches carry currents of $1.5\,\text{A}$ and $0.5\,\text{A}$. What is the total current entering the parallel combination?Answer: $2.0\,\text{A}$
4. In an ideal steady resistor circuit, what relationship holds between source power and resistor power?Answer: The power supplied by the source equals the total power dissipated by the resistors.
5. Why might other devices on shared wiring briefly dim when a high-current appliance starts?Answer: The increased current creates a larger voltage drop across the wiring resistance.