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How do you calculate the equivalent resistance ($R_{eq}$) of series resistors?
Add the individual resistances: $R_{\text{eq}, s} = \sum_{i} R_{i}$
How do you calculate the equivalent resistance ($R_{eq}$) of parallel resistors?
Use the reciprocal sum formula: $\frac{1}{R_{\text{eq}, p}} = \sum_{i} \frac{1}{R_{i}}$
How do you calculate the terminal voltage ($\Delta V_{\text{terminal}}$) of a real battery?
Subtract the voltage drop across the internal resistance from the emf: $\Delta V_{\text{terminal}} = \mathcal{E} - Ir$
What are the key differences between series and parallel resistor connections?
Series: Single path for current, current is the same through each resistor, resistances add directly. | Parallel: Multiple paths for current, voltage is the same across each resistor, reciprocal sum for equivalent resistance.
What are the differences between ideal and non-ideal batteries?
Ideal: Constant voltage, zero internal resistance. | Non-Ideal: Voltage drops with current, has internal resistance.
What are the differences between ideal and non-ideal ammeters?
Ideal: Zero resistance, no impact on circuit. | Non-Ideal: Small resistance, decreases measured current.
What are the differences between ideal and non-ideal voltmeters?
Ideal: Infinite resistance, no current draw. | Non-Ideal: Finite resistance, draws some current, affecting voltage measurement.
What is equivalent resistance ($R_{eq}$)?
The total resistance of a group of resistors, treated as a single resistor to simplify circuit analysis.
What is the electromotive force (emf, $\mathcal{E}$) of a battery?
The potential difference across the terminals of a battery when no current is flowing; the ideal voltage of the battery.
Define an ideal battery.
A battery that provides a constant voltage regardless of the current and has zero internal resistance.
Define an ideal ammeter.
An ammeter with zero resistance, so it doesn't affect the current it measures.
Define an ideal voltmeter.
A voltmeter with infinite resistance, so it doesn't draw any current from the circuit.
What is internal resistance (r) in a battery?
The resistance within a real battery that impacts the voltage it delivers, causing the terminal voltage to be less than the emf when current flows.