Sensitivity of a galvanometer

Hands-on
Lab 7

Sensitivity of a Galvanometer

Goal

To determine the current required for full-scale deflection of a galvanometer

Equipment

Digital multimeter
Galvanometer (from analog multimeter)
Breadboard
2 1-kW resistors
6 100-kW resistors
6-V battery pack
Clip leads

Summary of Method

You’ll first connect a series circuit of the 2 1-kW resistors and the battery pack. Then you’ll create your own voltmeter to measure the potential difference across one of the resistors. The voltmeter will be composed of a galvanometer in series with a chain of 100-kW resistors. You’ll measure the galvanometer deflection as a function of total voltmeter resistance. For comparison to the analog meter results, you’ll also use the digital multimeter to measure the potential difference.

You’ll use your measurements together with theoretical circuit equations to determine the current required to deflect the galvanometer full scale. You’ll then check your work by changing the load resistance, calculating the multiplier resistance required for full-scale deflection, and then testing the result.

Prelab

Make a diagram of the circuit, including the galvanometer with its multiplier resistance. Denote the series load resistors as R₁ and R₂ (don’t assume they’re equal), the multiplier resistance as R_m, and the galvanometer coil resistance as R_g. R₁ will be the resistor across which the voltmeter is placed. We’re using fresh batteries so that we can ignore their internal resistances in comparison to the load resistances. (For simplicity, you may use the symbol R_v to represent the combined galvanometer and multiplier resistances.)
Using Kirchhoff’s Laws, solve for the galvanometer current in terms of the given resistances and the terminal voltage of the battery. Express your result in simplest form. This equation will be used later to solve for the galvanometer current using measurements of the other quantities.
Rearrange your equation from 2) to obtain an equation for the multiplier resistance. This will be used later to solve for the multiplier resistance necessary to give a full-scale deflection for a given load resistance.

Method

IMPORTANT: Don’t connect the circuit to the battery until the instructor has checked your circuit.

Use the digital multimeter to measure the resistances of all the resistors, the resistance of the galvanometer coil, and the terminal voltage of the battery pack. Record and label these values clearly, using the same symbols as defined above.
Construct the circuit described previously. Use a chain of 6 100-kW resistors as the multiplier resistance.
Ask the instructor to check your circuit.
If the circuit checks out, connect the battery. If the galvanometer deflects the wrong direction, reverse the battery leads. You should get a small positive deflection.
Construct a table with 5 columns. The first three columns will be Multiplier Resistance, Galvanometer Deflection (read on the 0-5 scale to the nearest tenth of a minor division), and Digital Voltmeter Reading. Be sure to record measured values (as opposed to nominal values). The next 2 columns will be reserved for calculations. Label these Equivalent Resistance and Galvanometer Current.
Reduce the multiplier resistance by one 100 k resistor. Record the new set of measurements.
Repeat step 6 until the galvanometer deflection is between half- and full-scale. DON’T reduce the multiplier resistance beyond this point. Otherwise you run the risk of damaging the galvanometer.
Disconnect the battery. Go on to the Calculations.

Calculations

Significant figures are very important in this lab. Be wary of rounding errors.

What is the percentage change in the galvanometer deflection over the full range of multiplier resistances used?
Compare the result of 1) to the percentage change in the digital meter reading over the same range of multiplier resistances. Explain any differences qualitatively.
Calculate the equivalent resistance of the entire circuit (including galvanometer branch). Start with a formula and show your substitutions.
Using prelab equation 2) and your data for the highest multiplier resistance, calculate the galvanometer current. Start with the equation, show your substitutions, and give the final result.
Record the values calculated in 4) and 5) in your table.
Repeat your calculations of current and equivalent resistance for the other multiplier resistances. Don’t show these calculations. Simply record them in the table.
In Graphical Analysis, plot a graph of Galvanometer Current vs. Scale Reading. Fit a straight line to the data. Document your graph and data table clearly. Print the graph and data table, and tape them into your lab book.
Using the equation of fit from 7), calculate the current required for full-scale deflection of the galvanometer. We will call this the sensitivity of the meter.

Check

The purpose of this last section is to check your work.

Each student will be given a new value for R₁ in the range of 2-10 kW. Using equation 3) of the prelab and the calculated galvanometer sensitivity, calculate the multiplier resistance needed for full-scale deflection of the galvanometer. Assume that all other circuit components (resistors and power supply) remain the same. Remember that the multiplier resistance doesn’t include the galvanometer resistance.
Now replace the existing R₁ in the circuit with the new one. Replace the multiplier resistance with the value calculated in step 1). This may require finding a combination of resistors that will yield the desired value to 3 significant figures.
Measure the battery voltage and record the value. If this value has changed significantly from the value that you used in step 1), you’ll need to recalculate the multiplier resistance.
Connect the battery to the circuit and record the galvanometer deflection.
Calculate the percentage difference between the measured deflection and the expected value of 5.00.

Discussion and Conclusion

Summarize what you did and what you found in this lab. Discuss errors that could contribute to differences between experimental and theoretical values.

Hands-on Lab 7