 # Basic Electronics Ninth Edition Grob Schultz

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Basic Electronics Ninth Edition Grob Schultz

Series Parallel Circuits
Basic Electronics Ninth Edition 6 CHAPTER Series Parallel Circuits ©2003 The McGraw-Hill Companies

Topics Covered in Chapter 6
Finding REQ for series-parallel resistances Resistance strings in parallel and banks in series Analysis of series-parallel circuits The Wheatstone bridge Opens and shorts in series-parallel circuits

Sections of Series-Parallel Circuits
Series components can be called a string. Parallel components can be called a bank. Series-parallel circuits combine strings and banks. A string can have parallel sections. A branch can have series sections.

A series string V

Another series string V

The series strings are in parallel and act as branches. Series strings
V

There are three branches in this
circuit; sections 1 and 2 are series strings. 1 2 3 V

There are three series sections in this
circuit; sections 1 and 2 are banks. 1 2 3 V

Comparison of Series and Parallel Circuits Voltage and Current
Series Circuit Current is the same in all components. V across each series R is I ´ R. Parallel Circuit Voltage is the same across all branches. I in each branch R is V/R.

I is constant in this section. V

I is constant in this section. V

V is constant across the branches.

Determining Current Flow
IT = 2 A + 1 A + 2 A = 5 A IT 2 W 10 W I3 I3 = 20 V 5 W + 3 W + 2 W = 2 A 10 W 3 W 20 V I1 = 20 V 10 W = 2 A I1 I2 I2 = 20 V 10 W + 10 W = 1 A 10 W 5 W REQ = VT IT = 20 V 5 A = 4 W

Determining REQ Directly
1 10 + 2 W 1 10 1 20 + 10 W 10 W 3 W 10 W 5 W 1 REQ = = 0.25 REQ = 4 W

Comparison of Series and Parallel Circuits Resistance and Conductance
Series Circuit RT = R1+R2+R3+…etc. RT must be greater than the largest individual R. Parallel Circuit GT = G1+G2+G3+…etc. GT must be more than the largest branch G. REQ must be less than the smallest branch R.

Determine REQ for the banks, then for the entire circuit.
4 W 5 W 20 W 1 W 5 W 10 W 10 W REQ = 4 W + 1 W + 5 W = 10 W

Determine the Total Current.
5 W 20 W 1 A 1 W 10 V 10 W 10 W IT = REQ VT = 10 V 10 W = 1 A

Determine the Voltage Drops.
5 W V = IR = 1V V = IR = 1 A x 4 W = 4 V 4 V 20 W 1 A 1 W 10 V V = IR = 1 A x 5 W = 5 V 5 V 10 W 10 W Use Ohm’s Law, IT, and bank REQ to find the bank drops. KVL check: 4 V + 1 V + 5 V = 10 V

Determine Bank Currents.
I(5 W) = 4 V 5 W = 0.8 A 0.8 A 5 W I(20 W) = 4 V 20 W = 0.2 A 0.2 A 20 W 4 V 1 A 1 W V = IR = 1V 10 V 5 V 10 W 10 W KCL check: 0.8 A A = 1 A

Comparison of Series and Parallel Circuits Miscellaneous Notes
Series Circuit Applied voltage is divided into IR voltage drops. The largest IR drop is across the largest R. Parallel Circuit Main-line current is divided into branch currents. The largest branch I is in the smallest branch R.

Wheatstone Bridge When R1/R2 = R3/R4 the bridge is balanced.
V = 0 When the bridge is balanced, V = 0. R4 R2 30 W 300 W When R1/R2 = R3/R4 the bridge is balanced.

Using a Wheatstone Bridge to Measure an Unknown Resistance
RX R1 RX = RS x R1 R2 V = 0 RS R2 3k W RS is a standard resistor and is calibrated. 300 W RS is adjusted to make V = 0. The unknown resistor is 3 kW x (100/300) = 1 kW

An Open in a Series-Parallel Circuit
Normal current, drops, and power dissipation in these two branches V appears across the open V V

An Open in a Series-Parallel Circuit
Total current is smaller Lower drops here (and less dissipation) Higher drop here Increased dissipation in the good resistor 2 3 & 4 V

A Short in a Series-Parallel Circuit
2 The total current and total power increase. Normal current, drops, and power dissipation in these two branches. The drop and power increase here. 3 V

A Short in a Series-Parallel Circuit
Total current is larger. Total power is larger. Higher drops here (and more dissipation) Zero drop here Zero dissipation in the good resistor 3 4 & 5 V