Shortcut Methods
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 colorcoded 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 colorcoded 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?
$$\tau = \frac{L}{R} = \frac{10 H}{20 \Omega} = 0.5 s$$