Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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(c) The circuit in Figure 2.1 is a simple voltage-divider configuration that uses two resistors in series to create
an output voltage, Vo which is a fraction of the input voltage, V₁. The basic circuit laws dictate that the
circuit current, I and the resultant voltage division output, Vo of this basic circuit configuration can be
expressed as:
Pre-Lab workspace
Vo
Table 2.1
| =
I
V₁
Rx + Ry
=
+ O
If the input voltage, V₁= 15 volts, and resistors Rx = 10 k and Ry = 5.0 k, find the values of the output
voltage, Vo and the circuit current, I by using the above expressions. Record the results in Table 2.1.
Rx
Vo
Ry
Ry
Vo =
Vo
Ry
Ry + Rx
.V₁
Figure 2.1: Simple voltage-divider circuit
Rx
Ry
Vo
For the resistor values selected for circuits in Figure 2.0 and Figure 2.1, and comparing your results in Table 2.0
with those in Table 2.1, answer the following questions:
(i) Why would the value of I = I₁ and Vo = V₂ (or V³)? Explain.
(ii) Would it be reasonable to conclude that resistor, Ry value chosen must be equivalent to the value of parallel
resistors, R₂ and R3 combined? Why?
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Transcribed Image Text:(c) The circuit in Figure 2.1 is a simple voltage-divider configuration that uses two resistors in series to create an output voltage, Vo which is a fraction of the input voltage, V₁. The basic circuit laws dictate that the circuit current, I and the resultant voltage division output, Vo of this basic circuit configuration can be expressed as: Pre-Lab workspace Vo Table 2.1 | = I V₁ Rx + Ry = + O If the input voltage, V₁= 15 volts, and resistors Rx = 10 k and Ry = 5.0 k, find the values of the output voltage, Vo and the circuit current, I by using the above expressions. Record the results in Table 2.1. Rx Vo Ry Ry Vo = Vo Ry Ry + Rx .V₁ Figure 2.1: Simple voltage-divider circuit Rx Ry Vo For the resistor values selected for circuits in Figure 2.0 and Figure 2.1, and comparing your results in Table 2.0 with those in Table 2.1, answer the following questions: (i) Why would the value of I = I₁ and Vo = V₂ (or V³)? Explain. (ii) Would it be reasonable to conclude that resistor, Ry value chosen must be equivalent to the value of parallel resistors, R₂ and R3 combined? Why?
(b) The simple DC circuit in Figure 2.0 is powered by a 15 volts DC battery input-source (V₁) which will cause
currents to flow through the resistors, R₁, R₂ and R3 as illustrated. When current flows through a resistor, it
creates a voltage across the resistor as governed by the Ohm's Law expression, V = I.R. The Kirchhoff's
Current Law (KCL) states that the sum of all currents entering (or leaving) a node is zero. Therefore, I₁ +
(- 1₂) + (-13) = 0, resulting in I₁ = I₂ + 13.
Even though the basic circuit laws may not be fully covered in class as yet, you may use the above circuit
law expressions to determine the missing values in Table 2.0. Show your analysis on the below workspace
provided. Note: 1 mA = 1x10-³A = 0.001A; and 1 kQ=1x10³Q=1000Q
Pre-Lab workspace
V₁
(15 volts)
V₂
V3
5 volts
←4₂₁₂
Table 2.0
+
I₁
R₁ (10 km)
www
V₁
Figure 2.0: Simple D.C. circuit for voltage and current measurements
R₂
(10 kn)
I₂
0.5 mA
↓
13
+
R3
(10 ΚΩ)
What relationship exists between voltages V₂ and V3? and between currents, I2 and 13? Why?
Was the voltage relationship V₁ = V₁ + (V₂ or V3) established? If so, why would it be the case?
If the resistor, R₁ is replaced with a wire (i.e. make R₁ = 0 22), intuitively what might the resultant value of the
voltage, V3 be? Explain.
expand button
Transcribed Image Text:(b) The simple DC circuit in Figure 2.0 is powered by a 15 volts DC battery input-source (V₁) which will cause currents to flow through the resistors, R₁, R₂ and R3 as illustrated. When current flows through a resistor, it creates a voltage across the resistor as governed by the Ohm's Law expression, V = I.R. The Kirchhoff's Current Law (KCL) states that the sum of all currents entering (or leaving) a node is zero. Therefore, I₁ + (- 1₂) + (-13) = 0, resulting in I₁ = I₂ + 13. Even though the basic circuit laws may not be fully covered in class as yet, you may use the above circuit law expressions to determine the missing values in Table 2.0. Show your analysis on the below workspace provided. Note: 1 mA = 1x10-³A = 0.001A; and 1 kQ=1x10³Q=1000Q Pre-Lab workspace V₁ (15 volts) V₂ V3 5 volts ←4₂₁₂ Table 2.0 + I₁ R₁ (10 km) www V₁ Figure 2.0: Simple D.C. circuit for voltage and current measurements R₂ (10 kn) I₂ 0.5 mA ↓ 13 + R3 (10 ΚΩ) What relationship exists between voltages V₂ and V3? and between currents, I2 and 13? Why? Was the voltage relationship V₁ = V₁ + (V₂ or V3) established? If so, why would it be the case? If the resistor, R₁ is replaced with a wire (i.e. make R₁ = 0 22), intuitively what might the resultant value of the voltage, V3 be? Explain.
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