A Galvanometer as a milliammeter

To get credit, always show your work and explain the number of significant digits you use

Part I. A Galvanometer as a milliammeter

 

1. a) Let’s start with the simplest circuit: the one in Figure 1. Set it up and have it checked by your instructor before closing it.

 

Use a single 1.5V battery. Use the multimeter to measure it emf:   ……1.505………….V

 

As the maximum allowed current for the galvanometer is 1.0 mA, set the resistance at at least

1.5 kW.

 

1. b) Change R so that the current I changes in steps of 0.1mA and fill the table below. (3 points)

 

R (W)	I (A)	RxI (units= W   )	1/I (A-1)
1,440	1.00e-3	1.44	1.000e3
1,610	0.90e-3
1,850	0.80e-3
2,130	0.70e-3
2,510	0.60e-3
3,050	0.50e-3

 

Why is the product RxI (almost) constant? (1 point)

STRAIGHT LINE

 

1. c) Plot R (vertical axis) versus 1/I (horizontal axis) (6 points) and find slope and intercept (with units).

 

Slope:                                                                                                               (1 point)

 

intercept:                                                                                                          (1 point)

 

What is the physical meaning of the slope?  (1 point)

 

 

Does the value you found make sense? Explain  (1 point)

 

 

What is the physical meaning of the intercept? (hint: what elements of the circuit have internal resistances?)  (1 point)

Part II.Conversion of a Galvanometer into a Voltmeter

 

2. a) Let’s now switch to the circuit in Figure 2. Set it up and have it checked by your instructor before closing it. For RABuse the rheostat (from the greek ῥέω “flow”) at its maximum resistance of 280W.

 

Calculate the resistance RM needed to make your 0-1.0 mA galvanometer work as a 0-3V voltmeter (neglect RG) and insert it in the circuit.

 

RM =     3000.     (units:     )                                                    (1 point)

 

1. b) Use your voltmeter to measure the voltage of 1 and 2 batteries in series.

 

V₁=.45…(A)*RM  =                (units:      )                 (1 point)

 

V₂= 0.85……(A)*RM  =                (units:      )         (1 point)

 

Measure V₁ and V₂ using a multimeter

 

V₁^m= 1.338…………………..  V

 

V₂^m= 2.87………………….   V

 

Compare the two couples of measurements:

 

V₁-V₁^m=                                                                                (1 point)

 

V₂-V₂^m=                                                                                 (1 point)

 

Are the measurements you made with the galvanometer in accord with the theory? Explain.

 (1 point)

 

Reducing the resistance RAB changes the measured voltages? Some change can be seen when the rheostat resistance is very low. Explain (hint: remember that the battery has an internal resistance). Calculate the current I_g and consider the two cases RAB » r and RAB @  r.(2 points)

 

Part III.Internal resistance of the galvanometer

 

1. a) Set up the circuit in Figure 4 and have it checked by your instructor before closing it.

 

For R₁ take one of the extra decade boxes.

 

1. b) with R₂ disconnected, vary R₁ until you get a full scale deflection (1.0mA)

 

1. c) Insert R₂ and adjust it until the meter deflection is reduced by ½. The value of R₂ is with good approximation RG.

 

RG= 65……….. W

 

Explain why (hint: R₁ is large, while we know that RG is small. Is the total current very sensitive to the insertion of R₂?) Use the relevant formulas to justify your answer.  (2 points)

Compare the value of RG thus obtained with the magnitude of the intercept of the graph in part I.

Which is larger?  (1 point)

Can you explain why? (1 point)