An ideal 12 V battery is connected to a circuit containing resistor RA=10Ω in series with a parallel network of two resistors, RB=20Ω and RC=30Ω. A switch allows an additional resistor RD=15Ω to be connected in parallel with RB and RC.
Assume all resistors are ohmic and the temperature remains constant.
(a) Calculate the equivalent resistance of the circuit when the switch is OPEN (so RD is not connected).
(b) Determine the total current supplied by the battery in the configuration described in part (a).
(c) The switch is now CLOSED, adding RD in parallel with RB and RC. Calculate the new equivalent resistance of the entire circuit.
(d) Using your result from part (c), compute the new total current supplied by the battery.
(e) Explain, without further calculation, how the current through RA compares between the two configurations and why this result follows from your answers above.