Can someone help me to answer the following?
(b) The circuit shown in Figure 1 can be used to measure the resistance of a platinum resistance thermometer (PRT). AB is a uniform resistance wire of length 1.0 m and C is a sliding contact on this wire. A standard resistor R is included in the circuit. The position of C is adjusted until the voltmeter V reads zero.
(i) By applying Kirchhoff’s laws to loops ADCA and BCDB, deduce an expression for the resistance of the PRT in terms of l1, l and the value of the standard resistor.
----------------------------
I have tried a few times and ended up with an expression PRT=R*l1/(L-l1). But im worried I am not using the loop rule correctly.
Im sorry you cannot see the circuit as I cant post links to this on here.
Thank you for any help.
To help you solve this problem, let's break it down step-by-step.
First, let's understand the circuit setup described:
- A circuit with a uniform resistance wire AB of length 1.0 m.
- Point C is a sliding contact on the wire AB.
- There is a standard resistor R included in the circuit.
- The position of C is adjusted until the voltmeter V reads zero.
Now, let's approach the problem using Kirchhoff's laws:
1. Apply Kirchhoff's first law (the junction rule) to loop ADCA:
- At point A, the current splits into two branches: one through the PRT and the other through the standard resistor.
- At point C, the current forms a junction and recombines.
- There is no other current input or output in this loop, so the total current entering point A is equal to the total current leaving point A.
- We can write this as: I1 = I2, where I1 is the current passing through the PRT and I2 is the current passing through the standard resistor.
2. Apply Kirchhoff's second law (the loop rule) to loop BCDB:
- Starting at point B and following the path through the standard resistor, we encounter a change in potential (+IR) due to the resistance (Ohm's law).
- Moving from C to D along the PRT, we encounter a change in potential (-l1I1), where l1 is the distance from point C to D.
- Finally, moving from D back to B, there is no change in potential (since the voltmeter V reads zero).
- According to Kirchhoff's second law, the sum of the potential changes around a closed loop is zero.
- We can write this as: IR - l1I1 = 0.
Now, let's combine these equations to solve for the resistance of the platinum resistance thermometer (PRT):
From Kirchhoff's first law: I1 = I2 (Equation 1)
From Kirchhoff's second law: IR - l1I1 = 0 (Equation 2)
To find the resistance of the PRT, we need to express I1 and I2 individually in terms of the voltage V across the voltmeter and the resistance R:
From Ohm's law: V = IR (Equation 3)
From Equation 1, we can substitute I1 = I2 into Equation 2:
V/l1 - V/R = 0
Multiply both sides by l1R to eliminate the denominators:
VR - l1V = 0
Now, solve for V:
VR = l1V
V(R - l1) = 0
Since V cannot be zero (as mentioned), R - l1 must be zero:
R = l1
Therefore, the expression for the resistance of the platinum resistance thermometer is:
PRT = R = l1
Hence, the correct expression for the resistance of the PRT in terms of l1 and the value of the standard resistor R is PRT = l1.
Please note that without the specific values of l1 and R, it is not possible to calculate the resistance of the PRT numerically. However, the above deduction provides the general expression.