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:
$$L = \frac{\Phi}{I}$$
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L: inductance in henries (H)
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Φ: magnetic flux in webers (Wb)
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I: current in amperes (A)
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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
$$\tau = \frac{L}{R}$$
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τ: time constant in seconds (s)
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L: inductance in henries (H)
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R: resistance in ohms (Ω)
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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:
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Some inductors have a color-coded band that indicates their inductance value.
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The first two bands indicate the first two digits of the inductance value.
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The third band indicates the multiplier.
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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?
$$\tau = \frac{L}{R} = \frac{10 H}{20 \Omega} = 0.5 s$$