Series Circuits ENTC 210: Circuit Analysis I Rohit Singhal Lecturer Texas A&M University

Is this a series circuit? R1R1 R2R2

R1R1 R2R2 R3R3

R1R1 R2R2 R3R3

Series Circuit Two elements are in series if  They have only one terminal in common.  The common point in the two elements is not connected to a third current carrying element.

Resistance Resistance is proportional to length length direction of current flow

Resistance R = ρ L/A ρ is the resistivity of the material (units?)

Resistance What happens if two elements are connected back to back? length direction of current flow length direction of current flow

Resistance R = ρ (L 1 +L 2 )/A R = R 1 + R 2 The total resistance of a series circuit is the sum of all the resistances in the path

Resistance The resistance seen by the source R=R 1 +R 2 The two circuits on the right are equivalent R1R1 R2R2 R 1 +R 2

Voltage Drop? The current through each resistor is calculated by the Ohm’s law  =V 1 /R 1  Where V 1 is the voltage across the resistor.  =V/R T  Where R T is the total resistance in the circuit. V 1 = VxR 1 /R T

Power? Power dissipated in each resistor  P 1 = V 1 2 /R 1  P 1 = (V 2 /R T 2 )x R 1 Total power = V 2 /R T = P 1 + P 2 + …

Kirchhoff’s Voltage Law The algebraic sum of the potential rises and drops around a closed loop is zero.

KVL V + V 1 +V 2 = 0 Can anyone prove this mathematically? R1R1 R2R2 V V1V1 V2V2

Voltage Divider Rule In a series circuit the voltage across the resistive elements will divide as the magnitude of the resistors

Ground Terminal This is not a loop.  Or is it?

Ground Terminal This is not a loop.  Or is it? Ground terminal means that the two points are both connected to ground and are at a zero potential.  So this is a loop.

Internal Resistances Voltage and other sources have internal resistances, and they should be counted while solving circuits.