Question #026bf

2 Answers
May 18, 2017

#13.85Omega#

Explanation:

To find out the resultant Resistance please refer the Image below which gives better illustration about the diagram enter image source here

now instead of directly substituting the values we we use there names .
and #R_("th")# is Thevenin’s equivalent resistance which is equal to
enter image source here
The resistance across A and B gives the value of Thevenin’s resistance or #R_("th")#

May 18, 2017

#V_"Thevenin"~~ 6.5V#
#R_"Thevenin" = 19.3Omega#

Explanation:

To find the Thevenin Voltage, you remove the load and then compute the open circuit voltage across the two points

Summing the voltages around the first window:

#(R_1+ R_3)I_1-R_3I_2 = V_1" [1]"#

Summing the voltages around the second window:

#-R_3I_1+ (R_3+R_2+R_5)I_2 = 0" [2]"#

Substituting values:

#15OmegaI_1-5OmegaI_2 = 69V" [3]"#
#-5OmegaI_1+ 23OmegaI_2 = 0" [4]"#

Multiply equation [4] by 3 and add to equation [3]:

#64OmegaI_2=69V#

#I_2=69/64A#

#V_(R_5)= I_2R_5#

#V_(R_5)= (69/64A)(6Omega)#

#V_(R_5)~~ 6.5V#

Because no current flows through #R_4# with #R_L# removed, the voltage across #R_5# is the Thevenin equivalent voltage:

#V_"Thevenin"~~ 6.5V#

To find the Thevenin equivalent resistance, we replace the voltage source with a wire and compute the equivalent resistance:

#R_"Thevenin" = R_4+ 1/(1/R_5+1/(R_2+1/(1/R_3+1/R_1))#

#R_"Thevenin" = 15Omega+ 1/(1/(6Omega)+1/(12Omega+1/(1/(5Omega)+1/(10Omega)))#

#R_"Thevenin" = 19.3Omega#