A technician makes a network from five resistors and joins a battery to it at the points A and C, as the figure shows. She wants a single resistor that would draw the same current from the same battery if it replaced the whole network. Which value of resistance should she choose? Think carefully about whether any current passes through the resistor between B and D.

Fig. 1: A network of five resistors joined as a diamond between the points A on the left and C on the right. From A, the upper path goes through a 3.0 ohm resistor to the top corner B and then through a 5.0 ohm resistor to C. The lower path goes through a 6.0 ohm resistor to the bottom corner D and then through a 10 ohm resistor to C. A 7.0 ohm resistor joins B to D.