Parallel dc Circuits - Circuit Analysis - Lecture Slides, Slides of Electrical Circuit Analysis

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Chapter 6 – Parallel dc Circuits

6.1 - Introduction

There are two network configurations – series

and parallel.

In Chapter 5 we covered a series network. In

this chapter we will cover the parallel circuit

and all the methods and laws associated with

it.

Parallel Resistors

 For resistors in parallel, the total resistance is

determined from

 Note that the equation is for the reciprocal

of RT rather than for RT.

 Once the right side of the equation has been determined, it is necessary to divide the result into 1 to determine the total resistance

Parallel Resistors

 For parallel elements, the total conductance is the sum of the individual conductance values.

As the number of resistors in parallel increases, the input current level will increase for the same applied voltage.  This is the opposite effect of increasing the number of resistors in a series circuit.

GT = G 1 + G 2 + G 3 +...+ G N

Parallel Resistors

For equal resistors in parallel:

Where N = the number of parallel resistors.

Parallel Resistors

 A special case: The total resistance of two

resistors is the product of the two divided by

their sum.

The equation was developed to reduce the effects of the inverse relationship when determining R T

6.3 – Parallel Circuits

Voltage is always the same across parallel

elements.

V 1 = V 2 = E

The voltage across resistor 1 equals the voltage across resistor 2, and both equal the voltage supplies by the source.

Parallel Circuits

 For single-source parallel networks, the source current (I s ) is equal to the sum of the individual branch currents.

I s = I 1 + I 2

 For a parallel circuit, source current equals the sum of the branch currents. For a series circuit, the applied voltage equals the sum of the voltage drops.

6.4 – Power Distribution in a Parallel Circuit

 For any resistive circuit, the power

applied by the battery will equal that

dissipated by the resistive elements.

PE = PR 1 + PR 2 + PR 3 +...+ PR N

 The power relationship for parallel resistive

circuits is identical to that for series resistive

circuits.

6.5 - Kirchhoff’s Current Law

 Kirchhoff’s voltage law provides an important relationship among voltage levels around any closed loop of a network.  Kirchhoff’s current law (KCL) states that the algebraic sum of the currents entering and leaving an area, system, or junction is zero.  The sum of the current entering an area, system or junction must equal the sum of the current leaving the area, system, or junction.

∑ Iin =^ ∑ Iout

6.6 – Current Divider Rule

 The current divider rule (CDR) is used to find

the current through a resistor in a parallel circuit.

General points:

 For two parallel elements of equal value, the current will divide equally.  For parallel elements with different values, the smaller the resistance, the greater the share of input current.  For parallel elements of different values, the current will split with a ratio equal to the inverse of their resistor values.

Current Divider Rule

T x

T x I R

R I =

Voltage Sources in Parallel

 Two batteries of different terminal voltages

placed in parallel

 When two batteries of different terminal voltages are placed in parallel, the larger battery tries to drop rapidly to the lower supply  The result is the larger battery quickly discharges to the lower voltage battery, causing the damage to both batteries

6.8 - Open and Short Circuits

 An open circuit can have a potential difference (voltage) across its terminal, but the current is always zero amperes.