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 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?

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