Electricity and Electric Circuits
Read circuit relationships, combine resistors, interpret electrical data, and connect power calculations to real devices and safety.
Electricity and Electric Circuits
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Start with the circuit path, then apply voltage, current, and resistance relationships
In a series circuit, there is one path: current is the same through every component, resistances add, and voltage is divided. In a parallel circuit, branches share the same two nodes: voltage is the same across each branch, branch currents add, and equivalent resistance is smaller than the smallest branch resistance.
An ammeter has very low resistance and is placed in series. A voltmeter has very high resistance and is placed in parallel across the component being measured.
Track what stays the same
Series → same current. Parallel → same voltage. Write this before calculating.
Equivalent resistance predicts total current
Adding resistance in series raises equivalent resistance. Adding another parallel path lowers equivalent resistance and can increase total source current.
Reduce the circuit from the inside out
Series group: Add the resistances.
Parallel pair: Use 1/Req = 1/R₁ + 1/R₂, or Req = R₁R₂/(R₁ + R₂).
Then: Find total current from I = V/Req. Expand the circuit again to find branch voltages and currents.
Final check: Parallel branch currents must add to the total current.
Why it works
Trying to solve every branch simultaneously causes avoidable errors. Reduction converts a complicated network into a single source-and-resistance problem before working backward.
Five forms you should recognize
Problem: A 12 V source is connected across 4 Ω.
I = 12/4 = 3 AProblem: Resistors of 2 Ω and 4 Ω are in series across 12 V.
Req = 6 Ω; I = 12/6 = 2 AThe voltage drops are 4 V and 8 V.
Problem: Resistors of 6 Ω and 3 Ω are in parallel.
Req = (6×3)/(6+3) = 2 ΩProblem: A device uses 2 A at 12 V.
P = 12(2) = 24 WProblem: A 1 kW appliance runs for 0.5 h.
E = 1(0.5) = 0.5 kWhCheck before you commit
- Adding parallel resistances directly
- Dividing current equally between unequal parallel branches
- Putting an ammeter across a battery
- Putting a voltmeter in series
- Confusing power in watts with energy in kilowatt-hours
- Forgetting that total current increases when more parallel loads are added
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Electricity and Electric Circuits FAQ
Why is parallel equivalent resistance smaller than either branch?
Adding a branch provides another path for charge, so the network allows more total current at the same voltage.
Does current get used up by a resistor?
No. Charge flow is conserved; the resistor transfers electrical energy to heat, light, or another form.
Why can an extension cord overload?
It carries the sum of appliance currents, and excessive current produces strong resistive heating.
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