# Revisiting Series-Parallel resistance

#### meanface

Joined Apr 9, 2015
9
I've been away from this for a very long time and I'm returning.
I'm stuck and need some assistance on this question:

Referring to the figure below, If Eout = 14.3 volts, what is the applied voltage, E?

(which steps and formulas are used to calculate this ?)

THANK YOU

#### MikeML

Joined Oct 2, 2009
5,444
.
(which steps and formulas are used to calculate this ?)
Ohm and Kirchoff

#### meanface

Joined Apr 9, 2015
9
Ohm and Kirchoff
would you mind showing where to plug the correct values ? I tried and thought I had it correct but i didnt. my book is saying 100 volts.
Thank You

#### DickCappels

Joined Aug 21, 2008
9,620
Start with how much current it takes to get 14.3 volts across R4, then figure out how much voltage you need on the left side of R3 in order to get that much current. The work out what is happening with R2 and R1.

#### meanface

Joined Apr 9, 2015
9
Start with how much current it takes to get 14.3 volts across R4, then figure out how much voltage you need on the left side of R3 in order to get that much current. The work out what is happening with R2 and R1.
Thanks, I tried that but I guess i did something wrong. i still dont have 100v

#### Jony130

Joined Feb 17, 2009
5,439

#### DickCappels

Joined Aug 21, 2008
9,620
What did you get for the voltages at the nodes?

#### peterpv

Joined Apr 9, 2015
1
Easy if you know how
I want to determine the ratio Eo / E (the attenuation of the circuit from left (input) to right(output) )
for that I first determine the attanuation from E to the internal node between R1,R2 and R3:
From this node to ground we have (R3 + R4) // R2: R3 + R4 = 40 + 10 = 50 ohms; parallel to R2: 1/(1/50 + 1/R2) = 1/ (1/50 + 1/20) = 14.286 ohms
So the attanuaton from E to the node between R1,R2 and R3: Enode / E = Rto_gnd / (Rto_gnd + Rto_input) = 14.286 / (14.286 + R1 ) = 14.286 / (14.286 + 5.7) = 0.7148
OK, now similar from the node between R1,R2 and R3 to the output:
Eout / Enode = Rto_gnd / (Rto_gnd + Rto_input) = R4 / (R3 + R4) = 10 / (10 + 40) = 0.2
So the total transfer Eout / E = 0.7148 * 0.2 = 0.1430
So 1 Volt at E would give 0.1430 Volt at Eout
But Eout is 14.3 Volt which is (surprise surpise ) 100 times larger so E was 100 Volt !

Since I'm used to this I just use the Eout / Ein = Rto_gnd / (Rto_gnd + Rto_input) formula directly.
You can use Kirchhoff and ohm's laws to proof this formula and never look back

Enjoy !

#### WBahn

Joined Mar 31, 2012
28,177
would you mind showing where to plug the correct values ? I tried and thought I had it correct but i didnt. my book is saying 100 volts.
Thank You
Herein lies your problem. You are looking for magical formulas and where to plug in which values instead of understanding the underlying concepts that will allow you to use very simple equations that you understand well enough that you don't have to memorize where to plug in what values.

Q1) Given Eout and R4, how much current is flowing in R4?
Q2) How much current is flowing in R3?
Q3) What is the voltage across R3?
Q4) What is the voltage at the junction of R1,R2,R3 (relative to the bottom node, which we'll define as 0V)?
Q5) How much current is flowing in R2?
Q6) How much current is flowing in R1?
Q7) What is the voltage across R1?
Q8) What is E?

#### meanface

Joined Apr 9, 2015
9
Easy if you know how
I want to determine the ratio Eo / E (the attenuation of the circuit from left (input) to right(output) )
for that I first determine the attanuation from E to the internal node between R1,R2 and R3:
From this node to ground we have (R3 + R4) // R2: R3 + R4 = 40 + 10 = 50 ohms; parallel to R2: 1/(1/50 + 1/R2) = 1/ (1/50 + 1/20) = 14.286 ohms
So the attanuaton from E to the node between R1,R2 and R3: Enode / E = Rto_gnd / (Rto_gnd + Rto_input) = 14.286 / (14.286 + R1 ) = 14.286 / (14.286 + 5.7) = 0.7148
OK, now similar from the node between R1,R2 and R3 to the output:
Eout / Enode = Rto_gnd / (Rto_gnd + Rto_input) = R4 / (R3 + R4) = 10 / (10 + 40) = 0.2
So the total transfer Eout / E = 0.7148 * 0.2 = 0.1430
So 1 Volt at E would give 0.1430 Volt at Eout
But Eout is 14.3 Volt which is (surprise surpise ) 100 times larger so E was 100 Volt !

Since I'm used to this I just use the Eout / Ein = Rto_gnd / (Rto_gnd + Rto_input) formula directly.
You can use Kirchhoff and ohm's laws to proof this formula and never look back

Enjoy !

WOW Thank You

#### meanface

Joined Apr 9, 2015
9
Herein lies your problem. You are looking for magical formulas and where to plug in which values instead of understanding the underlying concepts that will allow you to use very simple equations that you understand well enough that you don't have to memorize where to plug in what values.

Q1) Given Eout and R4, how much current is flowing in R4?
Q2) How much current is flowing in R3?
Q3) What is the voltage across R3?
Q4) What is the voltage at the junction of R1,R2,R3 (relative to the bottom node, which we'll define as 0V)?
Q5) How much current is flowing in R2?
Q6) How much current is flowing in R1?
Q7) What is the voltage across R1?
Q8) What is E?
Yes, You are correct. I appreciate your time,
Thank you

#### WBahn

Joined Mar 31, 2012
28,177
Easy if you know how
I want to determine the ratio Eo / E (the attenuation of the circuit from left (input) to right(output) )
for that I first determine the attanuation from E to the internal node between R1,R2 and R3:
From this node to ground we have (R3 + R4) // R2: R3 + R4 = 40 + 10 = 50 ohms; parallel to R2: 1/(1/50 + 1/R2) = 1/ (1/50 + 1/20) = 14.286 ohms
So the attanuaton from E to the node between R1,R2 and R3: Enode / E = Rto_gnd / (Rto_gnd + Rto_input) = 14.286 / (14.286 + R1 ) = 14.286 / (14.286 + 5.7) = 0.7148
OK, now similar from the node between R1,R2 and R3 to the output:
Eout / Enode = Rto_gnd / (Rto_gnd + Rto_input) = R4 / (R3 + R4) = 10 / (10 + 40) = 0.2
So the total transfer Eout / E = 0.7148 * 0.2 = 0.1430
So 1 Volt at E would give 0.1430 Volt at Eout
But Eout is 14.3 Volt which is (surprise surpise ) 100 times larger so E was 100 Volt !

Since I'm used to this I just use the Eout / Ein = Rto_gnd / (Rto_gnd + Rto_input) formula directly.
You can use Kirchhoff and ohm's laws to proof this formula and never look back

Enjoy !
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