Voltage Current Resistance

The three fundamental quantities of any electric circuit. Voltage is electrical pressure (measured in volts), current is the flow of charge (amps), and resistance opposes that flow (ohms).

Why It Matters

Every circuit analysis starts here. Whether you are sizing a resistor for an LED, calculating heat dissipation in a regulator, or debugging why a sensor reads wrong, you are applying Ohm’s law and Kirchhoff’s laws. Get these wrong and components burn, signals clip, or systems fail silently.

How It Works

The Water Analogy

Electrical	Water analogy
Voltage (V)	Water pressure (height of tank)
Current (I)	Flow rate (liters/sec through pipe)
Resistance (R)	Pipe narrowing (restriction)

Higher pressure (voltage) pushes more water (current) through the pipe. A narrower pipe (higher resistance) reduces flow for a given pressure.

Ohm’s Law

V = I x R
I = V / R
R = V / I

Power Equations

Power is the rate of energy dissipation. All four forms are equivalent:

P = V x I
P = I² x R      (useful when you know current through a resistor)
P = V² / R      (useful when you know voltage across a resistor)

A 100 ohm resistor with 12V across it dissipates 12²/100 = 1.44W. You need at least a 2W rated resistor or it will overheat.

Kirchhoff’s Voltage Law (KVL)

The sum of all voltages around any closed loop equals zero. What the source gives, the components consume.

         +12V
          |
        [R1 4k]  ← V_R1 = 8V
          |
    Vout--+
          |
        [R2 2k]  ← V_R2 = 4V
          |
         GND

KVL: +12 - 8 - 4 = 0  ✓

Kirchhoff’s Current Law (KCL)

All current entering a node must leave it. No charge accumulates.

     2mA →──┐
             ├──→ 3mA
     1mA →──┘

KCL: 2mA + 1mA - 3mA = 0  ✓

Voltage Divider

The most common sub-circuit in electronics. Two resistors in series split the input voltage proportionally.

      Vin
       |
      [R1]
       |
       +──── Vout = Vin x R2 / (R1 + R2)
       |
      [R2]
       |
      GND

Only valid when negligible current is drawn from Vout. If a load draws significant current, use a buffer (Op Amps).

Series vs Parallel Resistance

Series (resistors in a chain): R_total = R1 + R2 + R3 + ...

Parallel (resistors side by side): 1/R_total = 1/R1 + 1/R2 + ...

Two-resistor shortcut for parallel: R_total = (R1 x R2) / (R1 + R2)

Reading Resistor Color Codes

Color	Digit	Multiplier
Black	0	x1
Brown	1	x10
Red	2	x100
Orange	3	x1k
Yellow	4	x10k
Green	5	x100k
Blue	6	x1M
Gold	-	x0.1 (tolerance 5%)
Silver	-	x0.01 (tolerance 10%)

Example: Brown-Black-Orange-Gold = 10 x 1k = 10k ohm, 5% tolerance.

Calculation Example

Design a voltage divider to get 3.3V from 5V for an MCU input:

vin = 5.0
vout_target = 3.3
 
# Choose R2 = 10k (common value), solve for R1
# Vout = Vin * R2 / (R1 + R2)
# R1 = R2 * (Vin/Vout - 1)
r2 = 10e3
r1 = r2 * (vin / vout_target - 1)  # 5.15k -> use 5.1k standard value
 
r1 = 5.1e3  # nearest standard value
vout = vin * r2 / (r1 + r2)        # 3.31V (close enough)
 
# Power dissipated
i = vin / (r1 + r2)                # 0.331 mA
p_r1 = i**2 * r1                   # 0.56 mW
p_r2 = i**2 * r2                   # 1.10 mW
p_total = vin * i                  # 1.66 mW (tiny, 1/8W resistors fine)
 
# Parallel resistance example
r_a, r_b = 10e3, 22e3
r_parallel = (r_a * r_b) / (r_a + r_b)  # 6.875k

Related

• Capacitors and Inductors — reactive components
• Transistors as Switches — controlling current with voltage
• Power Supply Design — regulating voltage for circuits
• Op Amps — buffering voltage dividers