Series, Parallel Networks and Kirchhoff's Laws
Resistances add in series and reciprocally in parallel; the junction rule conserves charge and the loop rule conserves energy.
What is Series, Parallel Networks and Kirchhoff's Laws?
Resistances add in series and reciprocally in parallel; the junction rule conserves charge and the loop rule conserves energy.
Key formula / rule: Series: R = R1 + R2. Parallel: 1/R = 1/R1 + 1/R2.
Key points
- Reduce series-parallel resistor networks.
- Apply Kirchhoff's laws to multi-loop circuits.
Common exam trap
Losing track of sign conventions while traversing a loop.
Definitions
- Term
Series, Parallel Networks and Kirchhoff's Laws
- Meaning
Resistances add in series and reciprocally in parallel; the junction rule conserves charge and the loop rule conserves energy.
- Term
Series, Parallel Networks and Kirchhoff's Laws — explanation
- Meaning
Kirchhoff's rules solve any network that series-parallel reduction cannot handle, provided sign conventions are applied consistently around each loop.
Learning objectives
Reduce series-parallel resistor networks.
Apply Kirchhoff's laws to multi-loop circuits.
Formulae
- Key point
Series: R = R1 + R2. Parallel: 1/R = 1/R1 + 1/R2.
- Key point
Junction rule: sum of currents in = sum of currents out.
- Key point
Loop rule: algebraic sum of potential changes around a loop is zero.
Prerequisites
PHY-U5-CUR-T1-S1-C1
Common mistakes
Losing track of sign conventions while traversing a loop.
Applying series-parallel reduction to a bridge network.
Keywords
Series
Parallel
Networks
Kirchhoff
Practice preview
Three resistors, 2 ohm, 3 ohm, and 5 ohm, are connected in series. What is their equivalent resistance?…
easy
Two resistors, 6 ohm and 3 ohm, are connected in parallel. What is their equivalent resistance?…
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According to Kirchhoff's Junction Rule (KCL), what is conserved at any junction in an electrical circuit?…
easy