Ohm’s Law, Power, and Series-Parallel Circuits
The Mathematics of DC Circuits
Ohm’s law and power
The basic relationship between voltage, current, and resistance is . Electrical power is , which can also be written as or . These formulas are the backbone of circuit analysis and component sizing.
Problem-solving habit
Before calculating, write down what is known, what is unknown, and the units. Most circuit mistakes come from unit confusion rather than math.
Series vs parallel
| Property | Series | Parallel |
|---|---|---|
| Current | Same through all components | Splits among branches |
| Voltage | Divides across components | Same across each branch |
| Equivalent resistance | ||
| Failure of one part | May open the whole path | Other branches may still work |
Two resistors of and are in series. What is the equivalent resistance?
Series resistances add directly: .
Correct answer:
If and , what is the voltage?
Using , we get .
Correct answer: 8 V
A supply is across a resistor. What power is dissipated?
Use ? Wait carefully: . So the correct answer is option 2.
Correct answer:
What is the total resistance of two equal resistors of in parallel?
For equal resistors in parallel, the equivalent resistance is half of one resistor: .
Correct answer: 5 Ω
Approach to network problems
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1
Step 1: Simplify obvious series or parallel groups.
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2
Step 2: Compute equivalent resistance one section at a time.
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3
Step 3: Find total current from .
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4
Step 4: Back-substitute to find branch voltages and currents.