Resistors in Parallel: Resistance

Total Resistance in Parallel Circuit

• When resistors are connected in parallel, the formula for finding the total resistance is:
  • $1 / R_{total} = (1 / R_1) + (1 / R_2) + (1 / R_3) + ...$

Explanation of the Formula

• In a parallel circuit, the total resistance $(R_{total})$ is calculated differently compared to series circuits.
• The formula considers the reciprocal of each individual resistance and adds them together.

Ohm's Law for Total Resistance

• Ohm's Law $(V = I * R)$ can be applied to understand resistance 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 Total Resistance

• To find the total resistance in a parallel circuit, you use the formula and take the reciprocal of the sum of the reciprocals of individual resistances.

Example Calculation

• If you have two resistors in parallel, $R_1 = 10 \Omega$ and $R_2 = 20 \Omega$:
• Calculate the total resistance:
  • $1 / R_{total} = (1 / 10 \Omega) + (1 / 20 \Omega)$
  • $1 / R_{total} = 0.1 + 0.05$
  • $1 / R_{total} = 0.15$
• To find $R_{total}$, take the reciprocal of 0.15:
  • $R_{total} = 1 / 0.15 = :highlight[6.67 \Omega]$ (approximately)

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Resistors in Parallel: Resistance

In Summary

• In a parallel circuit, the total resistance is calculated using the reciprocal formula.
• This formula takes into account the inverse of individual resistances.
• Ohm's Law (V = I * R) helps relate potential difference, current, and resistance in parallel circuits.
• Calculating total resistance in parallel is essential for understanding how current flows in complex circuits.