multi range voltmeter PDF

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Electric circuit with multi ranged voltmeter...

Description

A multi-range voltmeter could provides a greater number of workable ranges by connecting a number of resistors (multipliers) along with a range switch. The diagram above shows that the design of multi-range d’Arsonval voltmeter (with an internal resistance of 2 kΩ that requires a current of 5 mA to cause the meter to deflect full scale) that is able to measure the full range of the voltage across RL as the Ra, RL, and VS vary from minimum to maximum values. In this circuit,the DC voltage supply,VS is set as 2 V, 20 V and 200 V while the resistance of RL is set as 10 Ω, 50 Ω and 100 Ω. The multi-range d’Arsonval voltmeter in diagram above is using a five position switch(labeled 1, 2, 3, 4, 5) and four multipliers R1 (666.67 Ω) , R2 (4666.67 Ω) , R3 (18000.00 Ω) and R4 (24666.67 Ω) for voltage values V1, V2, V3, V4 and V 5. Resistance required for the multi-range d’Arsonval voltmeter(Ω) (VRL/Im)

VS (V)

RL (Ω)

I1(A) (VS/Rb+Rc+RL)

VRL(V) (I1 x RL)

2

10

0.03333

0.3333

66.67

2

50

0.02000

1.0000

200.00

2

100

0.01333 Table 1.1

1.3333

266.67

The table 1.1 above shows that the values of resistance required for the multi-range d’Arsonval voltmeter when VS is constant at 2 V while RL is set as 10 Ω, 50 Ω, 100 Ω. The values are calculated by using Ohm’s law, V = IR. However the biggest resistance requirement is only 266.67 Ω, this value is still lower than the internal resistance of d’Arsonval galvanometer (2 kΩ). Therefore, no resistance (multiplier) is needed for these 3 conditions. The first position switch is chosen.

VS (V)

RL (Ω)

I1(A) (VS/Rb+Rc+RL)

VRL(V) (I1 x RL)

Resistance required for the multi-range d’Arsonval

voltmeter(Ω) (VRL/Im)

20

10

0.33333

3.33333

666.67

20

50

0.20000

10.0000

2000.00

20

100

0.13333 Table 1.2

13.3333

2666.67

The table 1.2 above shows that the values of resistance required for the multi-range d’Arsonval voltmeter when VS is constant at 20 V while RL is set as 10 Ω, 50 Ω, 100 Ω. The values are calculated by using Ohm’s law, V = IR. The resistance requirement for the multi-range d’Arsonval voltmeter is 666.67 Ω and 2000.00 Ω when RL is set as 10 Ω and 50 Ω respectively. The values are lower and same with the internal resistance of d’Arsonval galvanometer (2 kΩ). Therefore, no resistance (multiplier) is needed for these 2 conditions. The first position switch is chosen. When RL is set as 100 Ω, the d’Arsonval voltmeter requires 2666.67 Ω of resistance. After the deduction of resistance required with the internal resistance of galvanometer, it still needs a total of 666.67 Ω. Therefore, the second position switch is chosen. Resistance required for the multi-range d’Arsonval voltmeter(Ω) (VRL/Im)

VS (V)

RL (Ω)

I1(A) (VS/Rb+Rc+RL)

VRL(V) (I1 x RL)

200

10

3.33333

33.3333

6666.67

200

50

2.00000

100.000

20000.00

200

100

1.33333 Table 1.3

133.333

26666.67

The table 1.3 above shows that the values of resistance required for the multi-range d’Arsonval voltmeter when VS is constant at 200 V while RL is set as 10 Ω, 50 Ω, 100 Ω. The values are calculated by using Ohm’s law, V = IR. The resistance requirement for the multi-range d’Arsonval voltmeter is 6666.67 Ω , 20000.00 Ω and 26666.67 Ω. The values are higher than the internal resistance of d’Arsonval galvanometer (2 kΩ). Therefore, resistance (multiplier) is needed for these 3 conditions. After the deduction of resistance required with the internal resistance of galvanometer, the resistance needed for these 3 conditions is 4666.67 Ω ,18000.00 Ω and 24666.67 Ω . The third, fourth and fifth position switch is chosen respectively....