Physics help (circuits) The resistance between points a and b in Figure P18.52 drops to five sixths its origin

Question

click fo picture http://www.webassign.net/sf5/p18_47.gif

The resistance between points a and b in Figure P18.52 drops to five sixths its original value when switch S is closed. Determine the value of R

Answer 1

R = 142 Ω.

Before closing the switch, resistance between a and b is

R + 100 II 100 = R + 50

After the switch is closed, it becomes

R + 2 × (90 II 10) = R + 18.

The statement specifies that this is 5/6 of the former figure, so

R + 18 = 5 /6(R + 50)
6R + 108 = 5R + 250
R = 250 - 108 = 142 Ω

Answer 2

Switch open Rab = R + 100||100

Switch closed Rab = R + 90||10 + 90||10