To determine the resistance of the shunt required for converting a voltmeter coil into an ammeter, we need to analyze the circuit configuration and apply Ohm's Law. Let's break this down step by step.
Understanding the Components
The voltmeter coil has a resistance of 50 ohms and is connected in series with a resistor of 1.15 kilo ohms (or 1150 ohms). Together, they can measure potential differences up to 12 volts. When we convert this setup into an ammeter, we will need to add a shunt resistor in parallel with the coil to allow the majority of the current to bypass the coil.
Calculating the Total Resistance
First, we need to find the total resistance of the voltmeter setup when measuring voltage. The total resistance (R_total) is the sum of the coil resistance and the series resistor:
- R_coil = 50 ohms
- R_series = 1150 ohms
- R_total = R_coil + R_series = 50 + 1150 = 1200 ohms
Determining the Current through the Voltmeter
Next, we can find the current that flows through this setup when it reads the maximum voltage of 12 volts:
- Using Ohm's Law (V = I × R), we can rearrange it to find current (I):
- I = V / R_total = 12 volts / 1200 ohms = 0.01 amperes (or 10 mA)
Setting Up the Ammeter Configuration
When we convert this voltmeter into an ammeter, we want it to measure currents up to 2 amperes. The shunt resistor will allow most of the current to bypass the voltmeter coil, which can only handle 10 mA without damage.
Calculating the Shunt Resistance
Let’s denote the shunt resistance as R_shunt. The total current (I_total) flowing through the circuit will be 2 amperes. The current through the voltmeter coil (I_coil) remains at 0.01 amperes. Therefore, the current through the shunt resistor (I_shunt) can be calculated as:
- I_shunt = I_total - I_coil = 2 A - 0.01 A = 1.99 A
Now, we can use the voltage across the shunt resistor and the voltmeter coil to find the shunt resistance. The voltage across both resistors must be the same when they are in parallel. The voltage across the voltmeter coil when it reads 12 volts is:
- V_coil = I_coil × R_coil = 0.01 A × 50 ohms = 0.5 volts
Since the voltage across the shunt must also be 0.5 volts, we can use Ohm's Law again to find R_shunt:
- V_shunt = I_shunt × R_shunt
- 0.5 volts = 1.99 A × R_shunt
- R_shunt = 0.5 volts / 1.99 A ≈ 0.2513 ohms
Final Result
To summarize, the resistance of the shunt resistor needed to convert the voltmeter coil into an ammeter that can measure currents up to 2 amperes is approximately 0.2513 ohms. This allows the majority of the current to bypass the coil while still enabling accurate readings.
