Determine the equivalent resistances of the \"ladder\" of equal 205-ohm resistor

Question

Determine the equivalent resistances of the "ladder" of equal 205-ohm resistors shown in. In other words, what resistance would an ohmmeter read if connected between points A and B? Express your answer to three significant figures and include the appropriate units. What is the current through resistor a if a 60.0-V battery is connected between points A and B? Express your answer to three significant figures and include the appropriate units. What is the current through resistor b? Express your answer to three significant figures and include the appropriate units. What is the current through resistor C? Express your answer to three significant figures and include the appropriate units.

Explanation / Answer

starting from the right hand side:

3 resistors with resistance R are connected in series.

equivalent resistance=3*R ohms

it is connected in parallel with R.

net resistance-3*R*R/(3*R+R)=0.75*R

0.75*R is in series with 2 resistors with resistance R.

equivalent resistance=0.75*R+R+R=2.75*R

2.75*R is in parallel with R.

equivalent resistance=2.75*R*R/(2.75*R+R)=0.7333*R

0.7333*R is in series with R andR.

hence total resistance between A and B=0.7333*R+R+R=2.7333*R

using R=205 ohms,

net resistance between A and B=560.33 ohms

=5.603*10^2 ohms

part B:

as per ohm's law,

current=voltage/resistance=60/(560.33)=0.107 A

part C:

taking equivalent resistance till the point where only a,b,c and equivalnet reistance are connected.

then resistor b is connected in parallel to 2.75*R resistance

current through this parallel combination=current through a=current through c

=0.107 A

using current division,

current through resistor b=0.107*2.75*R/(2.75*R+R)=0.07852 A

=7.85*10^(-2) A

part d:

current through resistor C=0.107 A

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