(b) Write a symbolic expression for the sum of the voltages around Loop abda in terms of 1₁, 13, R₁ and R3. Note that I already set the sum equal to 0. Σv₁ =\ abda = 0 (c) Write a symbolic expression for the sum of the voltages around Loop bcdb in terms of 12, 14, R₂ and R4. Note that I already set the sum equal to 0. [vi bcdb = 0 (d) What can you conclude about the currents based on the junction rule? O 1₁ 13 and 12 = 14 O 1₁ = 1₂ and 13 = 14 O 1₁ 14 and 1₂ = 13 (e) Write a symbolic expression for the mystery resistance in terms of R₁, R₂, and R3. R4

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(b) Write a symbolic expression for the sum of the voltages around Loop abda
in terms of 1₁, 13, R₁ and R3. Note that I already set the sum equal to 0.
Σv₁ =
abda
= 0
(c) Write a symbolic expression for the sum of the voltages around Loop bcdb
in terms of 12, 14, R₂ and R4. Note that I already set the sum equal to
Σv₁ =
bcdb
= 0
(d) What can you conclude about the currents based on the junction rule?
O 1₁ = 13 and 1₂ = 14
O 1₁ 1₂ and 13 = 14
O 1₁ = 14 and 1₂ = 13
R4 =
(e) Write a symbolic expression for the mystery resistance in terms of R₁, R₂, and R3.
Transcribed Image Text:(b) Write a symbolic expression for the sum of the voltages around Loop abda in terms of 1₁, 13, R₁ and R3. Note that I already set the sum equal to 0. Σv₁ = abda = 0 (c) Write a symbolic expression for the sum of the voltages around Loop bcdb in terms of 12, 14, R₂ and R4. Note that I already set the sum equal to Σv₁ = bcdb = 0 (d) What can you conclude about the currents based on the junction rule? O 1₁ = 13 and 1₂ = 14 O 1₁ 1₂ and 13 = 14 O 1₁ = 14 and 1₂ = 13 R4 = (e) Write a symbolic expression for the mystery resistance in terms of R₁, R₂, and R3.
The circuit shown in the diagram, called a Wheatstone Bridge,
is a device used to measure an uknown electrical resistance.
Resistors R₁ and R₂ have known resistances, and R3 is an
adjustable resistor known as a potentiometer (hence the arrow).
The middle resistor, r, is just there to make sure the ammeter (A)
doesn't get trashed. Resistor R4 is the mystery resistor.
The potentiometer resistance, R3, is adjusted until the current
through the ammeter is zero. At that point, the bridge is said to
be "balanced" and the value of the uknown resistance, R4, can be
determined from R₁, R₂, and R3. Pretty cool huh?
a
Apply Kirchoff's Loop Rule and Junction Rule to the Balanced Bridge.
R₁
R3
(a) When the bridge is balanced, the voltage between points b and d will be equal to
13
-Select--- ✓
-Select---
-128
-ε
zero
+½2€
+ε
(A)
E
R2
Transcribed Image Text:The circuit shown in the diagram, called a Wheatstone Bridge, is a device used to measure an uknown electrical resistance. Resistors R₁ and R₂ have known resistances, and R3 is an adjustable resistor known as a potentiometer (hence the arrow). The middle resistor, r, is just there to make sure the ammeter (A) doesn't get trashed. Resistor R4 is the mystery resistor. The potentiometer resistance, R3, is adjusted until the current through the ammeter is zero. At that point, the bridge is said to be "balanced" and the value of the uknown resistance, R4, can be determined from R₁, R₂, and R3. Pretty cool huh? a Apply Kirchoff's Loop Rule and Junction Rule to the Balanced Bridge. R₁ R3 (a) When the bridge is balanced, the voltage between points b and d will be equal to 13 -Select--- ✓ -Select--- -128 -ε zero +½2€ +ε (A) E R2
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