DC Circuit
The circuit that deals with direct current is called DC circuit.
Parallel DC Circuit:
When two or more electrical components are connected in a way that one end of each component is connected to a common point and the other end is connected to another common point, such an electrical DC circuit is referred as a parallel DC circuit.
Consider the electrical DC Parallel Circuit with three Resistors(R1,R2,R3) connected in parallel across a voltage source(V), as shown below:
The current has several parallel paths through these parallel connected components, so the circuit current will be divided into as many paths as the number of components.Let I (Ampere) be the total circuit current which is divided into current I1, I2 and I3 flowing through R1, R2 and R3 respectively. Now according to Ohm’s law:
Voltage drop across resistor R1, V = I1.R1
Voltage drop across resistor R2, V = I2.R2
Voltage drop across resistor R3, V = I3.R3
Voltage drop across whole parallel DC circuit, V = I1.R1 = I2.R2 = I3.R3
\[I_{1}=\frac{V}{R_{1}},I_{2}=\frac{V}{R_{2}}\; and\; I_{3}=\frac{V}{R_{3}} \]
I = I1 + I2 + I3 and as per Ohm’s law, I = V ⁄ R hence,
\[\frac{V}{R}=I_{1}+I_{2}+I_{3} \]
\[\frac{V}{R}=\frac{V}{R_{1}}+\frac{V}{R_{2}}+\frac{V}{R_{3}} \]
\[\frac{V}{R}=V\left [ \frac{1}{R_{1}}+\frac{1}{R_{2}}+\frac{1}{R_{3}}\right ] \]
\[\frac{1}{R}=\frac{1}{R_{1}}+\frac{1}{R_{2}}+\frac{1}{R_{3}} \]
