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Find the value of source current (I) from the circuit as shown below
- a)1 A
- b)2 A
- c)3 A
- d)4 A
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Find the value of source current (I) from the circuit as shown belowa)...
Concept:
Wheatstone Bridge:
- The Wheatstone Bridge has four resistors R1, R2, R3, and R4.
- A Voltage source is connected across one pair of diagonally opposite points A and C. This is called the battery arm.
- Between the other two vertices, B and D, a galvanometer G is connected. This is called the Galvanometer arm.
- For the sake of simplicity, let us assume that the cell has no internal resistance.
Balanced Bridge:
- The resistors are arranged in such a manner that the current through the galvanometer is zero, i.e. Ig = 0.
- The bridge is said to be balanced when deflection in the galvanometer is zero i.e. no current flows through the galvanometer or in other words VB = VD.
- Under the balanced condition,
- The above equation relates the four resistors is called the balance condition of the Wheatstone Bridge for which the galvanometer will show zero or null deflection.
Explanation:
According to the question given below:
- In the above figure, there are two sets of Balanced Wheatstone bridges.
- We know the condition for a balanced Wheatstone bridge is
- The condition holds true for both the equations mentioned above, therefore, the current in the 2 Ω and 3 Ω is zero.
- We can replace 2 Ω and 3 Ω from the circuit with an open circuit.
- The resistances of the top horizontal line are in series (Ignoring the 2 Ω branch, since no current passes through it).
⇒ Rtop = 2 Ω + 2 Ω = 4 Ω
- The resistances of the middle horizontal line are in series (Ignoring the 3 Ω resistance branch, since no current passes through it).
⇒ Rmidddle = 3 Ω + 3 Ω = 6Ω
- The resistances in the bottom horizontal line are in series.
⇒ Rbottom = 6 Ω + 6 Ω = 12 Ω
- The net resistance is (considering Rtop, Rmiddle, and Rbottom).
- The current through the battery (I) could be obtained by Ohm's Law,
Most Upvoted Answer
Find the value of source current (I) from the circuit as shown belowa)...
Concept:
Wheatstone Bridge:
- The Wheatstone Bridge has four resistors R1, R2, R3, and R4.
- A Voltage source is connected across one pair of diagonally opposite points A and C. This is called the battery arm.
- Between the other two vertices, B and D, a galvanometer G is connected. This is called the Galvanometer arm.
- For the sake of simplicity, let us assume that the cell has no internal resistance.
Balanced Bridge:
- The resistors are arranged in such a manner that the current through the galvanometer is zero, i.e. Ig = 0.
- The bridge is said to be balanced when deflection in the galvanometer is zero i.e. no current flows through the galvanometer or in other words VB = VD.
- Under the balanced condition,
- The above equation relates the four resistors is called the balance condition of the Wheatstone Bridge for which the galvanometer will show zero or null deflection.
Explanation:
According to the question given below:
- In the above figure, there are two sets of Balanced Wheatstone bridges.
- We know the condition for a balanced Wheatstone bridge is
- The condition holds true for both the equations mentioned above, therefore, the current in the 2 Ω and 3 Ω is zero.
- We can replace 2 Ω and 3 Ω from the circuit with an open circuit.
- The resistances of the top horizontal line are in series (Ignoring the 2 Ω branch, since no current passes through it).
⇒ Rtop = 2 Ω + 2 Ω = 4 Ω
- The resistances of the middle horizontal line are in series (Ignoring the 3 Ω resistance branch, since no current passes through it).
⇒ Rmidddle = 3 Ω + 3 Ω = 6Ω
- The resistances in the bottom horizontal line are in series.
⇒ Rbottom = 6 Ω + 6 Ω = 12 Ω
- The net resistance is (considering Rtop, Rmiddle, and Rbottom).
- The current through the battery (I) could be obtained by Ohm's Law,
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