Circuit connections lecture

1. CIRCUIT
CONNECTION
S

2. TERMS
• Network – is defined as the interconnection of components such as resistors and
batteries forming a complicated circuit.
• Branch – represents a single element such as voltage source or a resistor.
• Node – is the point of connection between two or more branches.
• Loop – is any closed path in a circuit.
• Mesh – is a loop which does not contain any other loops within it.

3.  Two elements are said to be in series if they are connected at
a single point and if there are no other current-carrying
connections at this point.
SERIES CONNECTION

4.  A series circuit is constructed by combining various
elements in series, as shown in Figure. Current will leave the
positive terminal of the voltage source, move through the
resistors, and return to the negative terminal of the source.
 The current is the same everywhere in a series circuit.
 R(total) = R1 + R2 + R3+… Rn
 V(total) = V1 + V2 + V3+… Vn
 Voltage Divider Rule:
𝑽𝒙 =
𝑹𝒙
𝑹𝒕
𝑬
SERIES CONNECTION

5. SERIES CONNECTION

6. SERIES CONNECTION –SAMPLE PROBLEM

7. Use the voltage divider rule to determine the voltage across each of the resistors in the
circuit shown.
SERIES CONNECTION –SAMPLE PROBLEM

8.  Elements or branches are said to be in a parallel connection
when they have exactly two nodes in common.
PARALLEL CONNECTION

9.  The voltage across all parallel elements in a circuit will be the
same.
𝑹𝑻 =
𝟏
𝟏
𝑹𝟏
+
𝟏
𝑹𝟐
+
𝟏
𝑹𝟑
+⋯
𝟏
𝑹𝒏
 𝑰𝑻 = 𝑰𝟏 + 𝑰𝟐 + 𝑰𝟑 + ⋯ 𝑰𝒏
Current Divider Rule:
𝐼1 =
𝑅2
𝑅𝑡
𝐼𝑡 ; 𝐼2 =
𝑅1
𝑅𝑡
𝐼𝑡
PARALLEL CONNECTION

10. PARALLEL CONNECTION –SAMPLE PROBLEM
Determine the total resistance of the resistor combinations of the Figures (a) and (b).
𝑅𝑇 =
𝑅1𝑅2
𝑅1 + 𝑅2
𝑅𝑇 =
1
1
𝑅1
+
1
𝑅2

11. SERIES – PARALLEL CONNECTION
Determine which resistors and branches are in parallel. Write an expression for the
total equivalent resistance Rt.

12. KIRCHHOFF’S LAWS
Kirchhoff’s Current Law (KCL)
 In any electrical network, the algebraic sum of the currents meeting at a point (or
junction) is zero.
 Incoming currents to a junction or point = outgoing currents from that junction or
point.
Kirchhoff’s Voltage Law (KVL)
 In any electrical network, the algebraic sum of the currents and resistances of
each conductors in any closed path (or mesh) in a network plus the algebraic sum
of the emfs in that path is zero.

13. SAMPLE PROBLEM

14. SAMPLE PROBLEM - SOLUTION

15. SAMPLE PROBLEM - SOLUTION

16. https://www.youtube.com/watch?v=TdUK6RPdIrA

17. KIRCHHOFF’S LAWS
Kirchhoff’s Current Law (KCL)
 In any electrical network, the algebraic sum of the currents meeting at a point (or
junction) is zero.
 Incoming currents to a junction or point = outgoing currents from that junction or
point.
Kirchhoff’s Voltage Law (KVL)
 In any electrical network, the algebraic sum of the currents and resistances of
each conductors in any closed path (or mesh) in a network plus the algebraic sum
of the emfs in that path is zero.

18. SAMPLE PROBLEM: For the circuit shown, find: (a) the currents Ia, Ib, and 𝐼𝐿;
(b) the load voltage 𝑉𝐿; (c) and the power dissipation, 𝑃𝐿