
The current flowing through the segment of the circuit shown in figure is
(A) from to
(B) from to
(C) from to
(D) from to

Answer
476.4k+ views
Hint: First, we can redraw the circuit diagram so that it is easy to identify the parallel resistances and the resistances in series with each other. We can apply the current divider rule to the circuit to find the solution.
Complete step by step answer:Let us first redraw the given circuit diagram as follows:
Here the points and are joined using a metal wire. Hence, the potential difference across the points and is zero. Thus
Let us define , , and . From the circuit diagram, the resistances and are connected parallel to each other. Similarly, the resistances and are connected parallel to each other.
The equivalent resistance of the resistances and can be written as
Here is the equivalent resistance of the resistances and .
Substituting the values for and in the above equation, we get
Again, we can write the equation for the equivalent resistance of the resistances and as
Here is the equivalent resistance of the resistances and .
Substituting the values for and in the above equation, we get
From the circuit diagram we can see that the combination of parallel resistances and is in series with the combination of parallel resistances and . Hence, we can write the equation for the equivalent resistance of the four resistances as,
Here is the equivalent resistance of the four resistances.
Now, we can substitute for and for in the above equation to get,
Now the total current flowing through the circuit can be written as
Here is the voltage across the circuit.
Since and , we can substitute the values for and to get the total current. Hence,
Now, using the current divider rule, we can write the equation for the current flowing between point to as,
Substituting the values for , and in the above equation, we get
Again, using the current divider rule, we can write equation for the current flowing from point to as,
Substituting the values for , and in the above equation, we get
Now, the current flowing through the segment can be written as
Here is the current flowing through the segment .
Now substituting the values of and , we get
Since, the current obtained has a positive value, we can confirm that the direction of the current is from to .
Therefore, the option (A) is correct.
Note:It should be noted that the resistances connected between two pints at the same potential difference are in parallel. Similarly, we should also note that the resistances connected between points at different potential differences are in series.
Complete step by step answer:Let us first redraw the given circuit diagram as follows:
Here the points
Let us define
The equivalent resistance of the resistances
Here
Substituting the values for
Again, we can write the equation for the equivalent resistance of the resistances
Here
Substituting the values for
From the circuit diagram we can see that the combination of parallel resistances
Here
Now, we can substitute
Now the total current flowing through the circuit can be written as
Here
Since
Now, using the current divider rule, we can write the equation for the current
Substituting the values for
Again, using the current divider rule, we can write equation for the current
Substituting the values for
Now, the current flowing through the segment
Here
Now substituting the values of
Since, the current obtained has a positive value, we can confirm that the direction of the current is from
Therefore, the option (A) is correct.
Note:It should be noted that the resistances connected between two pints at the same potential difference are in parallel. Similarly, we should also note that the resistances connected between points at different potential differences are in series.
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