Rm, All devices are connected in parallel. Because v alpha 0, a signal generator

Question

Rm, All devices are connected in parallel. Because v alpha 0, a signal generator is not needed, as in Problem 41. To begin the procedure, open circuit the decade box, or equivalency set R = R1 = infinity, a nd set the scale on the voltmeter to obtain a reasonable meter reading, say V m1 = E0, where the subscript "1" indicates our first meter reading. (For an analog meter, the reading should be almost full scale.) Next, reconnect the decade and decrease R until the meter reading drops to Vm2 = 0.5 E0. Record this value of R as R2. Suppose Rm = infinity. Show that Rth = R2. Suppose Rm is nonzero and finite. Show that Rth Rm/Rth + Rm = R2 and then solve for Rth. Then show that v oc = (1 + Rth/Rm)E0

Explanation / Answer

(a)In this part rm=infinite

so when you open circuit the decade box we get voltage around rth=vm1;vm1=E0.

   Reintroduce the decade box now  circuit is as follows

so the voltage around rth is 0.5E0.=>voltage around r is E0-0.5E0=0.5E0.

  therefore r=rth.

please see the comments for remaining answer

(b)voltmeter has an Rm in parallel that is why it did not come in picture(open circuit) in (a). but in second case Rm comes in parallel to rth .so equivalent resistance around Vm is Rth parallel to Rm.Let the reading be E0. now the voltage should be reduced to half(0.5E0) so R2 should have same value as Rth parallel to Rm. E0(measured value in voltmeter) is voltage around Rm.

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