Objective
State that, for a parallel circuit, the current from the source is larger than the current in each branch. 📈
Key Concepts
- In a parallel circuit, all branches share the same voltage from the source.
- The total current supplied by the source is the algebraic sum of the currents in each branch: \$I{\text{source}} = I1 + I2 + I3 + \dots\$
- Because each branch has a positive current, the source current is always greater than or equal to the current in any single branch.
- Ohm’s law applies to each branch: \$V = Ik Rk\$ where \$k\$ is the branch number.
Water‑Flow Analogy
Think of the electrical source as a water pump (🔋) and each branch as a pipe. The pump pushes water into all pipes at the same pressure (voltage). The total amount of water leaving the pump (source current) is the sum of the water flowing through each pipe (branch currents). Since water can’t disappear, the pump must supply more water than any single pipe can carry. 🚰
Illustrative Example
Consider a circuit with a 12 V source and three parallel resistors:
- \$R_1 = 4\,\Omega\$
- \$R_2 = 6\,\Omega\$
- \$R_3 = 12\,\Omega\$
Currents in each branch:
| Branch | Resistance (Ω) | Current (A) |
|---|
| \$R_1\$ | 4 | \$I_1 = \frac{12}{4} = 3\$ |
| \$R_2\$ | 6 | \$I_2 = \frac{12}{6} = 2\$ |
| \$R_3\$ | 12 | \$I_3 = \frac{12}{12} = 1\$ |
| Total Source Current | \$I_{\text{source}} = 3 + 2 + 1 = 6\$ A |
Notice that \$I_{\text{source}} = 6\$ A is greater than any individual branch current (3 A, 2 A, 1 A).
Exam Tips
- Always remember the relationship: \$I{\text{source}} = \sum I{\text{branches}}\$.
- When given a parallel circuit, calculate each branch current first, then sum them to find the source current.
- Check your units: current in amperes (A), resistance in ohms (Ω), voltage in volts (V).
- Use the water‑flow analogy to explain why the source current is larger.
- In multiple‑choice questions, look for statements that compare the source current with branch currents; the correct answer will state that the source current is greater.