Lecture 3

Simple Resistive Circuites

1

Resistors in Series

• Series-connected circuit elements carry the same current

• The seven resistors can be replaced by a single resistor

2

Resistors in Parallel

• Parallel -connected circuit elements have the same voltage across their terminals

3

Resistors in Parallel

Two resistors

4

Examples (Series): Page 99

5

Examples (Parallel): Page 99

30 Ω

Page 99

5 kΩ 80 Ω6

7

Solution

Use Ohm’s law, KCL & KVL

8

Voltage-divider circuits

9

10

Current-divider circuits

11

With load or without?

12

Measuring Voltage and Current

• An Ammeter: instrument to measure current.

• Placed in series with the circuit element whose current is being measured.

• A Voltmeter: instrument to measure voltage.

• Placed in parallel with the circuit element whose voltage is being measured.

• Two categories of meters used to measure voltage and current:

Digital meters and Analog meters

13

Measuring Resistance: The Wheatstone Bridge

Wheatstone bridge:

•is a circuit used to precisely measure resistance of medium values in the range of 1Ω to 1M Ω.

•Consists of four resistors, a dc voltage source, and a detector (galvanometer).

•One of the four resistors can be varied (R3).

To find the value of Rx, we adjust the variable resistor R3 until there is no current in the galvanometer. We then calculate the unknown resistor from the simple expression:

14

Measuring Resistance: The Wheatstone Bridge

When ig is zero, that is, when the bridge is balanced, KCL requires that:

Now, because ig is zero:•there is no voltage drop across the detector•Point a and b are at the same potential•KCL requires that

(1)

(2)

(3)

(4)

Combining (1) and (2) with (3):

(5)

Divide (5) by (4) and then solve for Rx:15

16

Delta-to-Wye (∆-to-Y)(Pi-to-Tee) equivalent circuits

The interconnected resistors can’t be reduced by the simple series or parallel equivalent circuits

A ∆ configuration viewed as π configuration A Y structure viewed as T structure

∆-to-Y equivalent circuit Y -to- ∆ equivalent circuit17

Please, solve assessment problem 3.8, page 9518