Question

The placement of resistors in a circuit is one factor that can determine the current passing through the resistor. You will be given three circuits, and for each circuit, you will be asked to compare the current through the various resistors.

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Rank the resistors in the figure below (A to D) on the basis of the current that flows through them. Rank from largest to smallest. To rank items as equivalent, overlap them.

Answer 1

B and C are in parallel
so their effective resistance =R/2
now A and combination of Band are in series
so the resistance =R+R/2=3R/2
this combination and D are in parallel so the total resistance=[R*3R/2] /5R/2=3R/5
current in the circuit=V/R=V/3R/5=5V/3R
current through the combination of A and B and C=5V/3R*R/5R/2=2V/3R
now current through D is 5V/3R-2V/3R=V/R
current after passing through A splits into two parts at the end ofA
now current through B=2V/3R*R/2R=2V/6R
and the current through C =2V/6R
now ranking
current through A=2V/3R
current through B=2V/6R
current through C=2V/6R
current through D=V/R
largest to smallest
D,A,C,B
B and C are equal