Resistance

Ohm’s law:

• $$V = IR$$

• V: voltage in volts (V)
• I: current in amperes (A)
• R: resistance in ohms (Ω)

Resistor color code:

• Each resistor has a color-coded band that indicates its resistance value.
• The first two bands indicate the first two digits of the resistance value.
• The third band indicates the multiplier.
• The fourth band indicates the tolerance.

Example: A resistor with brown, black, orange, and gold bands has a resistance of 10 ohms with a 5% tolerance.

Inductance

• Inductance:

$$L = \frac{\Phi}{I}$$

• L: inductance in henries (H)

• Φ: magnetic flux in webers (Wb)

• I: current in amperes (A)

• Lenz’s law: When the current in a coil changes, it induces a magnetic field that opposes the change in current.

Circuits with Resistance and Inductance

• Time constant

$$\tau = \frac{L}{R}$$

• τ: time constant in seconds (s)

• L: inductance in henries (H)

• R: resistance in ohms (Ω)

• The time constant is the time it takes for the current in a circuit to reach 63.2% of its final value when a voltage is applied or 36.8% of its initial value when the voltage is removed.

Inductor color code:

• Some inductors have a color-coded band that indicates their inductance value.

• The first two bands indicate the first two digits of the inductance value.

• The third band indicates the multiplier.

• The fourth band indicates the tolerance.

Example: An inductor with brown, black, orange, and gold bands has an inductance of 10 henries with a 5% tolerance.

Numerical Examples

• A circuit has a battery of 12 V and a resistor of 10 ohms. What is the current in the circuit?

$$I = \frac{V}{R} = \frac{12 V}{10 \Omega} = 1.2 A$$

• A coil has an inductance of 10 H and a resistance of 20 ohms. What is the time constant of the circuit?

$$\tau = \frac{L}{R} = \frac{10 H}{20 \Omega} = 0.5 s$$