Definition
A circuit consists of any number of elements have two common
terminals for all elements and providing more than one path that charge can
flow is called Parallel Circuit.
Suppose a number of resistors are connected together in a
circuit. So the resistors will be R1, R2, R3. And the circuit will be something
like this.
In this circuit, the resistors R1, R2, R3 have common two terminals
as marked in the picture. And if current “I” flows through this circuit then
the current will pass through in three different paths within the parallel connections.
So the current “I” will divide into three small currents
(I1, I2, I3) within parallel connections. But the voltage drop will generate
between two terminals of an electrical element. As the two terminals are
common for all elements in parallel connections that’s why the voltage drop will be the same for each element in parallel.
Equation
For a parallel connection, the total conductance is equal to the sum of individual components.
So,
Gt = G1+ G2+ G3+ G4+ … +Gn.
We know,
Conductance = 1/Resistance.
Or, G = 1/R
Therefore,
Mathematical Problem
Here, the resistance, R1=3Ω, R2= 5Ω, R3=6 Ω
Voltage, V= 5V
- What will be the total resistance and total conductance?
- What will be the voltages of individual branch V1, V2, V3?
- What will be the current I1, I2, I3 and source current is?
- Show that Is=I1+I2+I3
Solution:
- What will be the total resistance and total conductance?
As, Resistances R1= 3 Ω, R2= 5Ω, R3=6 Ω then,
Total resistance,
As, Conductance, G= 1/R
So, Gt = 1/Rt = (1/1.43)S = 0.69S
- What will be the voltages of individual branch V1, V2, V3?
As in parallel connection, the voltage across
elements are the same, So
V= V1=V2=V3
Or, V1=V2=V3=5V
I1 = V/R1 = (5/3) A= 1.67A
I2= V/R2= (5/5) A= 1A
I3= V/R3= (5/6) A= 0.83A
Source Current,
Is= (V/Rt)= (5/1.43) A = 3.496A ≈
3.5A
- Show that Is=I1+I2+I3
Source Current Is= 3.5A
And, I1+I2+I3= (1.67+1+0.83)A= 3.5A
So, Is= I1+I2+I3
So the final circuit will be,
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