Parallel Circuits

The Main Idea

Parallel Circuit is a circuit that is connected in parallel. All components in parallel circuit are linked to the same set of electric points, and they can create several branches(individual paths) within a circuit. These individual paths provide multiple pathways to the charge, so whenever the charge encounters a branch it would travel to the lower potential. This means adding an additional resistor in a parallel circuit would result in a decreased resistance. In a parallel circuit, the potential difference is identical with each resistor positioned in different branches. If a single circuit is opened(broke), no charge would flow to that path, but other paths will have charges going through them.

A Mathematical Model

[math]\displaystyle{ \frac{1}{R}_{Total}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...\frac{1}{R_N} }[/math]

When calculating the total Reisistance in a parallel circuit, we need to know the basic principle:

More resistor in parallel circuit, less resistance. So, we need to find the sum of reciprocals of individual resistors to derive the total resistor.

[math]\displaystyle{ V_{Total}=V_1=V_2=V_3...=V_N }[/math]

In a parallel circuit, potential difference through out the circuit is equal everywhere.

[math]\displaystyle{ I_{Total}=I_1+I_2+I_3+...I_N }[/math]

In a parallel circuit, the total amount of current outside the individual branch equals to the sum of individual branches in the circuit. Thus, the individual current in each branch depends on the resistor in the branch.

[math]\displaystyle{ I_1=I_{Total}\left( m_1 + m_2 \right) v \, }[/math].

A Computational Model

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