voltage Eo passes through the wire BD, in which there is an ammeter with resistance R.. B D Eo FIGURE 3.4.3 Wheatstone bridge (Problem 43). (a) Use Kirchoff's Current Law that rthe algebraic sum of the currents at each junction must be zero to show that the unknown currents /, I1. Iz, I3, and I, satisfy the lincar system I + l2 = I, I, + l3 = I, + l = /1, 2+!, = I3. (b) Kirchoff's Voltage Law states that the algebraic sum of all voltage drops around a closed circuit is zero." (Voltage equals resistance times current.) Use this law to show that R,I, – R313 – Rgk = 0. Rili + Rglg – R2l2 = 0, Ril, + R,I, = Eo. (c) Show that the bridge is balanced (that is, I = 0) when R, R3 = R2R.. 43. The Wheatstone Bridge The Wheatstone bridge is a device used to measure an unknown resistance R, by com- paring it with known resistances R,, R2, and Ry.$ The circuit diagram is shown in Fig. 3.4.3. The known resis- tances are adjusted so that no current from the cell with

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voltage Eo passes through the wire BD, in which there is
an ammeter with resistance R..
B
D
Eo
FIGURE 3.4.3 Wheatstone
bridge (Problem 43).
(a) Use Kirchoff's Current Law that rthe algebraic sum
of the currents at each junction must be zero to show
that the unknown currents /, I1. Iz, I3, and I, satisfy
the lincar system
I + l2 = I, I, + l3 = I,
+ l = /1, 2+!, = I3.
(b) Kirchoff's Voltage Law states that the algebraic
sum of all voltage drops around a closed circuit is
zero." (Voltage equals resistance times current.) Use
this law to show that
R,I, – R313 – Rgk = 0.
Rili + Rglg – R2l2 = 0,
Ril, + R,I, = Eo.
(c) Show that the bridge is balanced (that is, I = 0)
when R, R3 = R2R..
Transcribed Image Text:voltage Eo passes through the wire BD, in which there is an ammeter with resistance R.. B D Eo FIGURE 3.4.3 Wheatstone bridge (Problem 43). (a) Use Kirchoff's Current Law that rthe algebraic sum of the currents at each junction must be zero to show that the unknown currents /, I1. Iz, I3, and I, satisfy the lincar system I + l2 = I, I, + l3 = I, + l = /1, 2+!, = I3. (b) Kirchoff's Voltage Law states that the algebraic sum of all voltage drops around a closed circuit is zero." (Voltage equals resistance times current.) Use this law to show that R,I, – R313 – Rgk = 0. Rili + Rglg – R2l2 = 0, Ril, + R,I, = Eo. (c) Show that the bridge is balanced (that is, I = 0) when R, R3 = R2R..
43. The Wheatstone Bridge The Wheatstone bridge is a
device used to measure an unknown resistance R, by com-
paring it with known resistances R,, R2, and Ry.$ The
circuit diagram is shown in Fig. 3.4.3. The known resis-
tances are adjusted so that no current from the cell with
Transcribed Image Text:43. The Wheatstone Bridge The Wheatstone bridge is a device used to measure an unknown resistance R, by com- paring it with known resistances R,, R2, and Ry.$ The circuit diagram is shown in Fig. 3.4.3. The known resis- tances are adjusted so that no current from the cell with
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