There are certain kinds of circuits that one cannot analyze by grouping circuit

Question

There are certain kinds of circuits that one cannot analyze by grouping circuit elements into series and/or parallel sets. The diagram below shows such a circuit We can, however, still use Kirchhoff's laws to analyze this circuit. In this problem, we will see how The first step is to define some current directions. Since we aren't absolutely certain which direction current will flow in such a complicated circuit, we need to use signed numbers in to represent the current flowing through the nth element and define the direction of positive current flow for each element. The small arrows in the circuit below R1 and R4 and to the left of R5 define the (arbitrary) positive direction of current flow through these elements. You will define current directions for R2 and R3 shortly The next step is to apply the loop rule to various loops in the circuit. The diagram above shows two loops (L1 and L2) and provides an (arbitrary) definition for the direction of each loop. Since current always flows "downhill," the potential difference An across the nth element in the loop's direction is ??,--Rnin if in is positive when it flows in the loop's defined direction and Mn- +Roin if it is negative when it flows in that direction. Therefore, the loop rule applied to loop L n'n implies that (E7.16a) (a) Argue that with a suitable definition of the current directions through resistors R2 and R3 the analogous equation for loop L2 is (E7.16b) Describe the current directions for the resistors R3 and R4 that make this work, and explain your reasoning

Explanation / Answer

According to Above given equations

it is defined based on the Kirchoff current law (i.e.. It states that The current entering in the node is equal to the current leaving the node)

so we have different equations categorized in above as per the above questions in general

to proof the current direction flow for the Resistors R3 and R4 is given as the voltage source is towards the R4 the voltage drop across the resistor is I4xR4 and vice versa towards R3.

if Galvonometer or Deflection meter is not provided then current flowing through the R5 is zero when R4 is open circuit therefore I5=0:

so we can equate in that condition

R2=R4: R!=R3

so , Voltage drops across the resistor is I2R2=I4R4 and I1R1=I3R3 in that way we can define each current in a loop.

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