A rectangular conducting frame has vertices labeled consecutively A (upper left), B (upper right), C (lower right), and D (lower left). Resistor R1=15Ω occupies side AB, R2=30Ω occupies side BC, and R3=45Ω occupies side CD. Side DA is an ideal conductor with negligible resistance. A diagonal conductor BD includes a switch S.
A 24V battery is connected with its positive terminal at A and its negative terminal at D.
(1) Part 1: (a) With the switch S open, determine the number of independent closed loops available for current. List the loops by naming the sequence of vertices that forms each path.
(2) Part 2: (b) With switch S now closed, determine the new number of independent closed loops and list them.
(3) Part 3: (c) Identify which resistor(s) belong to more than one loop when S is closed. Provide reasoning based on the circuit’s geometry.
(4) Part 4: (d) An ideal ammeter is inserted somewhere along the diagonal BD after S is closed. State in which loop or loops the ammeter now resides, and explain qualitatively how its reading relates to the currents in the other loops.