Resistors in Parallel: Potential Difference

Potential Difference in Parallel Circuit

• When resistors are connected in parallel, they share the same potential difference across them.
• In a parallel circuit, components in parallel have identical potential differences.

Formula for Total Resistance (R_total) in Parallel

• To calculate the total resistance in a parallel circuit, use the reciprocal of the sum of the reciprocals of individual resistances.
• Mathematically, it's expressed as: $1 / R_{total} = (1 / R_1) + (1 / R_2) + (1 / R_3) + ...$

Ohm's Law for Potential Difference in Parallel

• Ohm's Law $(V = I * R)$ can be applied to understand potential difference in parallel circuits:
  • V represents potential difference (in volts, V).
  • I is the current (in amperes, A) in the circuit.
  • $R_1$, $R_2$, $R_3$ ... are the resistances of the branches.

Calculating Potential Difference

• In a parallel circuit, where the potential difference is the same across all branches:
• $V = I * R$
  • V is the potential difference.
  • I is the current.
  • R is the resistance of an individual branch.

Example Calculation

• If you have two resistors in parallel, $R_1 = 10 Ω$ and $R_2 = 20 Ω$, with a total current of $I = 2 A$:
  • The potential difference across $R_1 = 2 A * 10 Ω = :success[20 V]$
  • The potential difference across $R_2 = 2 A * 20 Ω = :success[40 V]$

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Resistors in Parallel: Potential Difference

In Summary

• In a parallel circuit, components share the same potential difference.
• Total resistance in a parallel circuit is calculated using the reciprocal formula.
• Ohm's Law (V = I * R) helps relate potential difference, current, and resistance in parallel circuits.
• Potential difference across individual components in parallel is determined by their resistance and the current in the circuit.