In the circuit shown in the figure below, R1 = 4.00 Ω, R2 = 3.00 Ω, and R3 = 6.00 Ω. Note that three currents are given.
(a) Find the current in the (center) 3.00 Ω resistor
b) Find the unknown emf's ε1 and ε2.
(c) Find the resistance R.
http://www.webassign.net/yf/27-31alt.gif

Question

In the circuit shown in the figure below, R1 = 4.00 Ω, R2 = 3.00 Ω, and R3 = 6.00 Ω. Note that three currents are given. 
(a) Find the current in the (center) 3.00 Ω resistor
b) Find the unknown emf's ε1 and ε2.
(c) Find the resistance R. 
http://www.webassign.net/yf/27-31alt.gif

noelgreco · Answer

Where do the currents going down on the right and left HAVE to go?

anonymous · Answer

towards the center where r2 is

radar · Answer

Use the node at the junction of R1, R2, and R3 as a reference node.  Now calculate the voltage drop across each of those resistors using Ohm's Law.  ER1 = IR =3*4 = 12 volts, 
ER2 = 8*3 = 24 volts and ER3 = 5*6 = 30 volts,  Noting the polarity that would result in E2 being 54 volts, and E1 being 36 volts.  That provides a voltage across R of 18 volts giving the value of R as 9 Ohms.  NoelGreco provided the info for calculating the current thru R2.