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Step 1:**Equal voltage distribution:** In a parallel circuit, the voltage across each component is equal to the source voltage.
Mathematically, we can express this as $$V_{component} = V_{source}$$.
This is because the voltage drop across each branch in a parallel circuit is the same, as they are all connected directly across the power source.
Step 2:**Total resistance calculation:** In a parallel circuit, the total resistance can be calculated using the formula \frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + ... + \frac{1}{R_n}, where R_1, R_2, ..., R_n are the individual resistances of each branch in the circuit.
This formula demonstrates that the total resistance in a parallel circuit is always less than the smallest individual resistance, resulting in a higher current flow compared to a series circuit with the same components.
Step 3:**Current division:** In a parallel circuit, the total current supplied by the source is divided among the branches, and the current flowing through each branch is inversely proportional to its resistance.
This can be represented by the formula $$I_{branch} = \frac{\frac{V_{source}}{R_{branch}}}{\frac{V_{source}}{R_{1}} + \frac{V_{source}}{R_{2}} + ... + \frac{V_{source}}{R_{n}}}$$.
This formula shows that the current flowing through a branch with lower resistance will be higher than the current flowing through a branch with higher resistance, assuming the voltage across all branches is the same (which is true for ideal voltage sources). **
Final Answer
The three rules concerning parallel circuits are: 1. Equal voltage distribution: V_{component} = V_{source} 2. Total resistance calculation: \frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + ... + \frac{1}{R_n} 3. Current division: I_{branch} = \frac{\frac{V_{source}}{R_{branch}}}{\frac{V_{source}}{R_{1}} + \frac{V_{source}}{R_{2}} + ... + \frac{V_{source}}{R_{n}}}
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