A rectangular bridge network consists of four resistors: and form the left and right…
PHYSICS · Multi-part · CBSE · Physics · Current Electricity · Current Electricity
Problem
A rectangular bridge network consists of four resistors: R1 and R2 form the left and right sides of the top branch, respectively, while R3 and R4 form the left and right sides of the bottom branch. The leftmost and rightmost vertical corners are connected to an ideal 9.0V battery (positive terminal on the left, negative on the right). A fifth resistor, R5, is connected horizontally between the midpoints of the two vertical sides, creating two interconnected loops that share R5. Assume currents circulate clockwise in the left loop (current IL through R1 and R3) and clockwise in the right loop (current IR through R2 and R4), with current I5 defined from left to right through R5.
(a) Starting from energy conservation for each independent loop, derive a symbolic expression for I5 in terms of the battery emf ε and the five resistances R1, R2, R3, R4, and R5. Your final expression should be fully simplified.
(b) Using ε=9.0V, R1=3.0Ω, R2=6.0Ω, R3=4.0Ω, R4=8.0Ω, and R5=5.0Ω, calculate the numerical value of I5 and indicate its direction (left → right or right → left).
(c) From your symbolic result in part (a), determine the general condition on the resistances under which I5 becomes zero, and interpret this condition in terms of potential differences in the circuit.
(d) Suppose R5 is replaced by an ideal ammeter having negligible resistance. Explain qualitatively how the reading of the ammeter would change as R2 is varied while all other resistances remain fixed, referencing the condition derived in part (c).