A simple circuit is made of a power source, a rheostat and an ohmic resistor. The potential difference across the resistor is initially 5.0 +/- 0.1 V. A good lab student measures the current across the resistor to be 1.65 +/- 5 mA.

a)If the student increases the voltage across the resistor to 9.0 +/- 0.1 V, around what value should the measurement of the current across the resistor be (include uncertainties)?

b)what was the purpose of the rheostat in the circuit?

Are you sure the 1.65 +/- 5 mA is correct? That could be any value between 6.65 mA and -3.35 mA.

Did you mean 1.65 A +/- 5 mA ?

The rheostat in the circuit allows the current in the resistor to vary with a fixed-voltage power source (like a battery).

The problem says 1.65 (plus on top and the minus sign below it) 5 mA

I think the plus and minus is the uncertainties.

How would you be going about it doing both values....
I have no idea how to solve it and what the outcome is?

a) To find the expected value for the current, we can use Ohm's Law, which states that the current (I) flowing through a resistor is equal to the voltage (V) across the resistor divided by its resistance (R). Mathematically, it can be written as I = V/R.

In this case, the potential difference across the resistor is 5.0 +/- 0.1 V and the current is 1.65 +/- 5 mA. To find the resistance, we rearrange Ohm's Law to solve for R: R = V/I.

First, let's convert the current measurement to Amps. 1 mA is equal to 0.001 A. Therefore, 1.65 mA is equal to 0.00165 A.

Now we can calculate the resistance using the initial potential difference and current:

R = (5.0 +/- 0.1 V) / (0.00165 +/- 0.00005 A)

To add or subtract uncertainties, we add or subtract the absolute values of the uncertainties. Therefore, the resistance can be calculated as:

R = (5.0 V) / (0.00165 A) = 3030.3 +/- (0.1 V / 0.00165 A) ≈ 3030.3 +/- 6.1 Ω

Now, let's calculate the expected current for the new potential difference of 9.0 +/- 0.1 V:

I = (9.0 +/- 0.1 V) / (3030.3 +/- 6.1 Ω) = 0.002970 +/- (0.1 V / 3030.3 Ω + 6.1 Ω / 3030.3 V) ≈ 0.002970 +/- 5.5 x 10^-6 A

Therefore, the expected value for the current across the resistor, with uncertainties, would be approximately 0.002970 +/- 5.5 x 10^-6 A.

b) The purpose of the rheostat in the circuit is to control the resistance in the circuit. By adjusting the rheostat, the resistance in the circuit can be increased or decreased, which in turn affects the current flowing through the circuit. The rheostat allows for variable resistance, allowing for the adjustment and control of the current in the circuit.