A bulb lights only when a cell, wires and the bulb are joined into a loop. That unbroken, closed path is an electric circuit.
Voltage is what drives the current, resistance is how strongly the circuit opposes it, and the three are tied together by Ohm's law, V = IR.
In the circuit above, raising the voltage makes the ammeter reading grow in the same proportion, and raising the resistance makes it shrink.
The graph below shows the same relationship as a straight line through the origin, and its slope is the resistance.
A Closed Path: the Electric Circuit
🔋 Picture It as Flowing Water
①Voltage is the height difference of a water tank: the bigger the difference, the harder the water is pushed
②Current is how much water flows each second: the amount of charge passing a cross-section of the wire
③Resistance is a narrow pipe: the narrower it is, the less water gets through
④The cell is like a pump that lifts the water back up
Circuit Diagrams and Meters
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Circuit diagram showing the ammeter and voltmeter readings as voltage and resistance change
6V
3Ω
💡 What the Sliders Show
①Doubling the voltage doubles the current
②Doubling the resistance halves the current
③The ammeter is connected in series with the circuit, and the voltmeter in parallel across the resistor
④With only one resistor, the voltmeter reads the full voltage of the cell
Ohm's Law as a Graph
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Current-voltage graph where the slope of the line is the resistance
Ohm's law
V = I × R
Voltage (V) = current (A) × resistance (Ω). With fixed resistance, current is proportional to voltage
Finding the current
I = VR
Current (A) = voltage (V) ÷ resistance (Ω)
Series and Parallel Connections
Series connection
Rtotal = R1 + R2 + R3 + ...
The current is the same everywhere and the total voltage is shared among the resistors. Adding resistors increases the total resistance
Parallel connection
1Rtotal = 1R1 + 1R2 + ...
Each resistor has the same voltage across it and the total current splits among the branches. Adding resistors decreases the total resistance
💡 Series and Parallel at Home
①Series: in a string of mini bulbs joined in one line, one broken bulb puts them all out
②Parallel: appliances in a home are connected in parallel, so switching one off leaves the rest on
③Because of this, every outlet has the same mains voltage (for example 220 V in Korea, 120 V in the US)
④Each appliance added in parallel increases the total current, which is why overloading a power strip is dangerous
Summary
Three Forms of Ohm's Law
V = IR, I = V/R, R = V/I
Knowing any two of voltage, current and resistance gives the third
🎯 Common Test Points
①Ohm's law V = IR: with fixed resistance, current is proportional to voltage
②On a graph with I across and V up, a steeper line means a larger resistance
③Series: same current, shared voltage, total resistance = sum of the resistances
④Parallel: same voltage, shared current, total resistance smaller than the smallest resistor
⑤An ammeter goes in series (low internal resistance); a voltmeter goes in parallel (high internal resistance)
Examples and Unit Review
Example 1
What is the total resistance when a 3 Ω and a 5 Ω resistor are connected in series?
1
In series the current passes through both resistors one after the other, so the total resistance is their sum (R = R₁ + R₂).
2
3 Ω + 5 Ω = 8 Ω.
▸ 8 Ω
Connected to 8 V, this circuit carries 8 V ÷ 8 Ω = 1 A, with 3 V across the 3 Ω resistor and 5 V across the 5 Ω resistor.
Example 2
How do the voltage across each bulb and the current through it differ between bulbs connected in series and in parallel?
1
In series the current has only one path, so it is the same everywhere, and the cell's voltage is shared among the bulbs.
2
In parallel each bulb is connected directly across the cell and gets the same voltage, while the current splits among the branches.
▸ Series: same current, shared voltage. Parallel: same voltage, shared current
That is why identical bulbs glow brighter in parallel: each one gets the full voltage of the cell.
Unit-test style
Which statement about series and parallel circuit connections is correct?
①In a series connection, the total resistance is the sum of the resistances
②In a series connection, the current is different through each bulb
③In a parallel connection, the voltage is different across each bulb
④In a series connection, if one bulb breaks the others stay lit
⑤Ohm law is V = I ÷ R
▸ ① In a series connection, the total resistance is the sum of the resistances
1
In a series connection the resistances add up, so the total resistance = R₁ + R₂ + ...
2
In series the current is the same everywhere (②), in parallel the voltage is the same (③), in series if one point breaks all go off (④), and Ohm law is V = IR (⑤).