Resistance and current
A resistor holds back the flow of charge. How hard it holds back is its resistance, measured in ohms (symbol Ω). This one is 450 ohms. The battery is set to 0 volts, so nothing flows yet.
Turn the battery up to 9 volts. Voltage is the push. Now charge flows round the loop, through the resistor and the meter and back. The meter shows the current: 20 milliamps (mA), which is 0.02 amps.
Ohm's law
Ohm's law links the three numbers: voltage equals current times resistance, V = I × R. Turn it round to get the current: I = V ÷ R. Here 9 V ÷ 450 Ω = 0.02 A, which is 20 mA.
Power is how fast energy is used: P = V × I, in watts (W). Here 9 V × 0.02 A = 0.18 W. A resistor turns that energy into heat, which is why it gets warm. Small resistors are often rated for ¼ W.
Swap in a 900 Ω resistor: double the resistance. The push stays 9 V, so the current halves: 9 ÷ 900 = 0.01 A, or 10 mA. The dashes slow, the needle drops and the resistor runs cooler, at 0.09 W.
The LED
Turn the battery down to 0 V and swap the jumper wire for a red LED (light-emitting diode). It does not follow Ohm's law. Past about 2 V, a little more push makes its current shoot up, and too much current burns it out.
A resistor in series limits the current. The LED needs about 20 mA and drops about 2 V. With 5 V, the resistor takes the rest: 5 − 2 = 3 V. So R = V ÷ I = 3 ÷ 0.02 = 150 Ω.
Turn the battery up to 5 V. Nothing flows until the push passes about 2 V; then the LED lights. At 5 V the meter reads 20 mA, the resistor carries 3 V, and it warms by only 0.06 W.
In detail
;; step 1/8 · resistance Resistance R, in ohms (Ω) 1 Ω = 1 volt per amp (1 V/A), the SI unit This resistor: R = 450 Ω Battery: 0 V, so no push and no current.
The board is a teaching model: the battery has no internal resistance, and the wires and the meter are ideal (no resistance), so the whole battery voltage sits across the resistor. Ohm's law holds for ohmic parts such as resistors, where current is proportional to voltage. Diodes, including LEDs, are nonohmic (OpenStax University Physics 2, section 9.4). The LED is drawn as a fixed 2.0 V drop once it conducts, a common first approximation. Kingbright's WP7113ID red LED lists 1.9 V typical at 10 mA (2.3 V maximum) and reaches 20 mA at about 2.0 V; its steady-current maximum is 30 mA. P = V × I = I² × R = V² ÷ R; in a resistor this energy leaves as heat (OpenStax, section 9.5). SparkFun notes that standard through-hole resistors usually come in ¼ W or ½ W ratings.