Voltage, Current, Resistance, and Power
Unit 2: Fundamentals of Electricity and Electronics. Lesson 8 of 60 in CBET Academy.
Every troubleshooting measurement you will ever make comes back to four quantities and one law.
The four quantities
- Voltage (V, volts): electrical pressure, the push. Measured across two points.
- Current (I, amperes): the flow of charge. Measured through a path.
- Resistance (R, ohms): opposition to flow. Measured with the power off.
- Power (P, watts): the rate energy is used, which usually becomes heat.
Ohm's law
V = I x R. Rearranged: I = V / R and R = V / I. Twelve volts across 4 ohms pushes 3 amps. If the resistance rises, the current falls. This is also why a shock's severity depends on skin resistance: 120 volts through dry skin at 100,000 ohms is about 1 mA, but through wet skin at 1,000 ohms it is 120 mA, a lethal current.
Power
P = V x I. Substituting Ohm's law: P = I squared x R, and P = V squared / R. A 120 V heater drawing 10 A dissipates 1,200 W. A resistor carrying too much current overheats because power rises with the square of the current.
Series circuits
Components in a single path. The same current flows through each; voltages add up to the source. Total resistance is the sum: R total = R1 + R2 + R3. If one component opens, the whole path stops, which is how a fuse works.
Parallel circuits
Components side by side across the same two points. The same voltage is across each; currents add. Total resistance is less than the smallest branch: 1 / R total = 1/R1 + 1/R2 + ..., or for two resistors (R1 x R2) / (R1 + R2). Two 100-ohm resistors in parallel make 50 ohms. Wall outlets are in parallel, which is why one lamp burning out does not darken the room.
Kirchhoff, in plain words
- Current into a junction equals current out.
- Voltages around any closed loop add up to zero: the drops equal the source.
These two rules let you find any unknown in a circuit from a schematic.
Worked example
A 24 V supply feeds a 6 ohm resistor and a 2 ohm resistor in series. Total resistance 8 ohms, current 24 / 8 = 3 A, voltage across the 6 ohm resistor 3 x 6 = 18 V, across the 2 ohm resistor 6 V, and 18 + 6 = 24. Power in the 6 ohm resistor is 3 squared x 6 = 54 W.
Voltage, Current, Resistance, and Power, explained slowly
Water in pipes, and why the analogy works
Voltage is water pressure. Current is the flow of water. Resistance is how narrow the pipe is. Power is how much work the flowing water does, which for electricity mostly means heat. Push harder (more voltage) and more flows; narrow the pipe (more resistance) and less flows. That is Ohm's law, and it is the whole basis of every voltage and resistance measurement you will ever take.
The law and its three forms
V
----- cover the one you want: V = I x R I = V / R R = V / I
I x R- 9 V battery across a 3 ohm lamp: I = 9 / 3 = 3 A.
- A heater draws 5 A from 120 V: R = 120 / 5 = 24 ohms.
- 2 A through a 50 ohm resistor: V = 2 x 50 = 100 V across it.
Power: where the heat comes from
P = V x I 120 V x 2 A = 240 W P = I squared x R (2 A) squared x 24 ohms = 96 W P = V squared / R (120 V) squared / 60 ohms = 240 W
The squared forms matter for troubleshooting: double the current through a resistor and it dissipates four times the heat. That is why a slightly overloaded component browns and fails, and why a resistor rated for a quarter watt in a circuit that now carries more current than designed is the one you find scorched.
Series: one path
+----[R1 = 6]----[R2 = 2]----+ | | 24 V | | | +----------------------------+
There is only one path, so the same current flows through everything. Resistances add: 6 + 2 = 8 ohms. Current: 24 / 8 = 3 A. Voltage drops: 3 x 6 = 18 V across R1, 3 x 2 = 6 V across R2, and 18 + 6 = 24, the source. Voltages add up to the source. Open any component and everything stops, which is exactly what a fuse is for. A string of old Christmas lights was a series circuit, which is why one bulb killed the string.
Parallel: several paths
+-----+-----+ | | | 12 V [R1] [R2] R1 = 6 ohms, R2 = 3 ohms | | | +-----+-----+
Every branch sees the same voltage, 12 V. Each draws its own current: 12/6 = 2 A and 12/3 = 4 A. Currents add: 6 A total. Total resistance is 12 / 6 = 2 ohms, smaller than the smallest branch, because adding a path always makes it easier for current to flow. The formula: 1 / R = 1/6 + 1/3 = 1/2, so R = 2. For two resistors, the shortcut (R1 x R2) / (R1 + R2) = 18 / 9 = 2. Wall outlets are parallel, so one dead device does not affect the others.
Kirchhoff, without the algebra
- What flows into a junction flows out. If 6 A enters a node and 2 A leaves on one branch, 4 A leaves on the other.
- Go around any loop and the voltage rises equal the voltage drops. The 24 V source in the series example is matched by 18 + 6 of drops.
These are the rules you use silently when you compare a measured voltage to the one printed on a schematic and decide which stage is wrong.
The shock connection
The body is a resistor, and Ohm's law decides how much current a voltage pushes through it.
120 V through dry skin, about 100,000 ohms: I = 120 / 100,000 = 1.2 mA a tingle 120 V through wet skin, about 1,000 ohms: I = 120 / 1,000 = 120 mA fibrillation range 120 V through a catheter to the heart, ohms in the hundreds: amps enough to kill instantly
Same voltage, three outcomes, because resistance changed. This is the whole reason wet locations, sweaty patients, and cardiac catheters get special rules.
How the exam asks it
- "A 12 V supply drives 3 A through a load; what is the resistance?" 4 ohms.
- "Two 100 ohm resistors in parallel?" 50 ohms.
- "In a series circuit, which quantity is the same through every component?" Current.
- "A resistor's current doubles; its power dissipation..." Quadruples.
What to memorize
- V = IR, P = VI = I squared R = V squared / R.
- Series: same current, voltages add, resistances add. Parallel: same voltage, currents add, resistance shrinks.
- Shock current = voltage / body resistance; wet skin is deadly at wall voltage.