Question

What is the formula for a parallel circuit?

Answer 1

In a parallel circuit, the components (like resistors, capacitors, or inductors) are connected in such a way that there are multiple paths for the current to flow. Here are the key formulas for a parallel circuit:

### 1. **Total Resistance (Rₜ) for Resistors in Parallel:**

The formula for total resistance in a parallel circuit is:

\[
\frac{1}{Rₜ} = \frac{1}{R₁} + \frac{1}{R₂} + \frac{1}{R₃} + \dots
\]

Where:
- \(R₁, R₂, R₃, \dots\) are the individual resistances of the resistors.

If there are only two resistors in parallel, the formula simplifies to:

\[
Rₜ = \frac{R₁ \cdot R₂}{R₁ + R₂}
\]

### 2. **Total Current (Iₜ) in a Parallel Circuit:**

The total current is the sum of the currents through each parallel branch:

\[
Iₜ = I₁ + I₂ + I₃ + \dots
\]

Where:
- \(I₁, I₂, I₃, \dots\) are the currents through each parallel resistor.

### 3. **Voltage Across Each Component:**

In a parallel circuit, the voltage across each component is the same and equal to the source voltage (\(Vₜ\)):

\[
Vₜ = V₁ = V₂ = V₃ = \dots
\]

Where:
- \(Vₜ\) is the total voltage of the power source.

### Key Points:
- The total resistance in a parallel circuit is always **less** than the smallest individual resistance.
- The total current is the sum of the currents through each branch.
- The voltage is the same across each component, unlike in series circuits where the voltage divides among the components.

Let me know if you'd like any more details on how these formulas are used!