Find  V_x (or  v_x(t)) and  I_x (or  i_x) using voltage division rule.
a)
Voltage Divider Problem - A
b)
Voltage Divider Problem - B
c)
Voltage Divider Problem - C
d)
Voltage Divider Problem - D

Solution

a)
Voltage Divider Problem - A
Voltage divider:  V_x=\frac{5\Omega}{2\Omega+5\Omega}\times 14 V=10 V
Ohm's law:  I_x=\frac{V_x}{5 \Omega}=2 A

b)
Voltage Divider Problem - B

Voltage divider:  V_x=\frac{4\Omega}{2\Omega+3\Omega+1\Omega+4\Omega}\times (-9 V)=-3.6 V
Ohm's law:  I_x=-\frac{V_x}{4 \Omega}=0.9 A
Please note that  I_x is leaving from the positive terminal of  V_x. Therefore, applying the Ohm's law results in  V_x=-R\times I_x.

c)
Voltage Divider Problem - C
Voltage divider:  v_x(t)=\frac{5\Omega}{2\Omega+5\Omega+3\Omega}\times (-5 \sin (2t))=-2.5 \sin (2t) V
Ohm's law:  i_x(t)=\frac{v_x(t)}{5 \Omega}=-\frac{1}{2} \sin (2t) A

d)
Voltage Divider Problem - D
The tricky part in this problem is the polarity of  V_x. In the defined formula for voltage divider, the current is leaving the voltage source from the positive terminal and entering to resistors from positive terminals. In this problem, the current is entering to the the resistor from the negative terminal. Therefore, the voltage for  V_x is the negative of the voltage obtained from the voltage divider formula. The reason is that another voltage can be defined with the inverse polarity and its value can be found using the voltage division rule.  V_x is the negative of the defined voltage because it represents the voltage across the same nodes with inverse polarity.
Voltage divider:  V_x=- \frac{5\Omega}{2\Omega+5\Omega}\times 10 V= - 7.143 V

Ohm's law ( I_x is entering from the negative terminal of  V_x):  I_x= - \frac{V_x}{5 \Omega}=1.428 A

.

Published by Yaz

Hi! Yaz is here. I am passionate about learning and teaching. I try to explain every detail simultaneously with examples to ensure that students will remember them later too.

Join the Conversation

4 Comments

Leave a comment

Leave a Reply to Yaz Cancel reply

Your email address will not be published. Required fields are marked *

This site uses Akismet to reduce spam. Learn how your comment data is processed.