The ammeter your physics instructor uses for in class demonstrations has a resistance R(g)= 60 ohms and requires a current of 1.0 mA for a full scale deflection. The same ammeter can be used to measure currents of much greater values by wiring a shunt resistor of relatively small resistance R(p) in parallel with the ammeter. The values of the shunt resistance that allows the ammeter to be measure a current of 12 A at a full scale deflection is
Vf = If*Rg = 0.001 * 60 = 0.06 Volts.
Rp = Vf / If = 0.060 / 12 = 0.005 Ohms.
Vf = Full-scale voltage.
If = Full-scale current.
To find the value of the shunt resistor (Rp) that allows the ammeter to measure a current of 12 A at full scale deflection, we can use the concept of parallel resistance.
The total current passing through the parallel combination of the ammeter and shunt resistor is the sum of the currents passing through each component. According to Ohm's Law, the current passing through the ammeter (Ia) is given by:
Ia = V / Ra
where V is the voltage applied across the circuit and Ra is the resistance of the ammeter. Since the ammeter requires a current of 1.0 mA (0.001 A) for full scale deflection, we have:
0.001 A = V / 60 Ω
Solving for V, we find that the voltage applied across the ammeter is 0.06 V.
To measure a current of 12 A, the total current passing through the circuit should be 12 A when the ammeter is at full scale deflection. Therefore, the current passing through the shunt resistor (Ip) is given by:
Ip = Itotal - Ia
where Itotal is the total current passing through the circuit (12 A) and Ia is the current passing through the ammeter (0.001 A).
Substituting the values, we have:
Ip = 12 A - 0.001 A
Ip = 11.999 A
Since the shunt resistor is in parallel with the ammeter, the voltage across the shunt resistor is the same as the voltage across the ammeter, which is 0.06 V. Therefore, using Ohm's Law, we can find the value of the shunt resistor (Rp):
Ip = V / Rp
Substituting the values, we have:
11.999 A = 0.06 V / Rp
Solving for Rp, we find:
Rp = 0.06 V / 11.999 A
Rp ≈ 0.005 ohms
Therefore, the value of the shunt resistance that allows the ammeter to measure a current of 12 A at full scale deflection is approximately 0.005 ohms.