A node N in a DC circuit receives current I0 from an external source and splits it into three parallel branches that contain resistors R1, R2, and R3, respectively. The three branches reconverge at node M, which is connected to the return path of the source through an ideal conductor. The resistors have the following numerical values: R1=2.0Ω, R2=5.0Ω, and R3=10.0Ω. Let the currents through the three resistors be I1, I2, and I3, respectively, each defined as flowing away from node N.
(a) Using only symbolic variables, derive an expression for the ratio I2I1 in terms of R1 and R2. State any assumptions you make in your derivation.
(b) Determine the numerical values of the current ratios I2I1, I3I1, and I3I2 for the given resistor values.
(c) If the total current entering node N is I0=6.0A, calculate the individual branch currents I1, I2, and I3.
(d) If resistor R3 is replaced by a new resistor R3′ such that I3 equals I2 while I0 and the other resistors remain unchanged, determine the required value of R3′.