A moving coil instrument has a resistance of 75 ohms and gives full scale deflection of 100 scale divisions for a current of 1mA. This instrument is connected in parallel with shunt resistance 25 ohms.The combination is then in series with load and a supply. What is the current through the load when the instrument gives an indication of 80 scale divisions?
instrument current ... (80/100) * 1 ma
shunt is 1/3 the resistance of the instrument
... so, three times the current
the two parallel currents add to equal the load current
I1 = (80/100)*1ma = 0.8 ma. = current thru instrument.
I2 = (75/25)*0.8ma = 2.4 ma = current thru 25 ohm resistor.
I1+I2 = 0.8+2.4 = 3.2 ma = current thru load.
Well, let's do some clown calculations here!
First, we need to figure out the current passing through the shunt resistor. Since the instrument gives a full-scale deflection of 100 scale divisions for a current of 1mA, we can assume that each division represents 1/100th of the full-scale deflection.
Therefore, when the instrument gives an indication of 80 scale divisions, the current passing through the shunt resistor would be 80/100 * 1mA = 0.8mA.
Now, since the shunt resistor and the moving coil instrument are connected in parallel, the current passing through them will be the same. So the current passing through the moving coil instrument would also be 0.8mA.
Next, we have the combined resistance of the moving coil instrument and the shunt resistor, which is 75 ohms || 25 ohms. The symbol "||" means parallel combination, not parallel universe.
So, the combined resistance would be (75 * 25) / (75 + 25) = 18.75 ohms.
Now we can calculate the current passing through the load. We just need to apply Ohm's Law, which states that I = V/R, or in this case, current = voltage / resistance.
Assuming we know the voltage across the load, we can divide it by the combined resistance to get the current. However, without knowing the voltage, we will have to consult a magician instead of a clown to perform some magic tricks and conjure the voltage value.
So, for now, the current through the load when the instrument indicates 80 scale divisions remains a mystery!
To determine the current through the load when the instrument gives an indication of 80 scale divisions, we need to consider the shunt resistance, the resistance of the moving coil instrument, and the full-scale deflection current.
1. Calculate the current through the moving coil instrument at full-scale deflection:
The resistance of the instrument is given as 75 ohms, and the full-scale deflection current is given as 1 mA. Using Ohm's Law (V = IR), we can find the voltage across the instrument:
V = I * R
V = 1 mA * 75 ohms
V = 75 mV (millivolts)
2. Determine the current through the shunt resistance:
The shunt resistance is given as 25 ohms, and the voltage across the shunt can be calculated using the voltage across the instrument (75 mV) and the full-scale deflection current (1 mA) as follows:
V_shunt = I_shunt * R_shunt
75 mV = I_shunt * 25 ohms
I_shunt = 75 mV / 25 ohms
I_shunt = 3 mA (milliamperes)
3. Calculate the effective current passing through the combination of the instrument and the shunt:
Since the instrument and the shunt resistance are connected in parallel, the total current passing through the combination is the sum of the instrument current (1 mA) and the shunt current (3 mA):
Total current = Instrument current + Shunt current
Total current = 1 mA + 3 mA
Total current = 4 mA
4. Determine the current through the load when the instrument gives an indication of 80 scale divisions:
Since the instrument follows a linear scale, we can assume that the current through the load is proportional to the number of scale divisions. Therefore, the current through the load when the instrument indicates 80 scale divisions is:
Current through load = (80 / 100) * Total current
Current through load = (80 / 100) * 4 mA
Current through load = 3.2 mA (milliamperes)
Therefore, the current through the load when the instrument gives an indication of 80 scale divisions is 3.2 mA.
To calculate the current through the load when the instrument gives an indication of 80 scale divisions, we need to follow these steps:
1. Determine the full-scale current: The instrument gives a full-scale deflection of 100 scale divisions for a current of 1mA. So, the full-scale current of the instrument is 1mA.
2. Calculate the shunt current: The shunt resistance is connected in parallel to the instrument. The shunt resistance is given as 25 ohms. We can use Ohm's Law (V = IR) to calculate the current flowing through the shunt. The voltage across the shunt is the same as the instrument voltage. The resistance of the instrument is given as 75 ohms. So, the current through the shunt is (1mA * 75 ohms) / (25 ohms + 75 ohms) = 0.75mA
3. Calculate the total current flowing through the combination: The shunt current branches off from the main current. So, the total current flowing through the combination is the sum of the shunt current and the current through the load. Let's assume the current through the load is I_load.
Total current = shunt current + I_load
Total current = 0.75mA + I_load
4. Determine the ratio of the scale divisions to the current: We know that the full-scale deflection of 100 scale divisions corresponds to a current of 1mA. Therefore, the ratio of scale divisions to current is 100 divisions / 1mA.
5. Use the ratio to calculate the current for 80 scale divisions: To find the current through the load for 80 scale divisions, we can use the ratio calculated in step 4. Multiply the scale divisions (80) by the ratio to get the corresponding current.
Current for 80 scale divisions = 80 divisions * (100 divisions / 1mA)
So, the current through the load when the instrument gives an indication of 80 scale divisions is the total current minus the shunt current:
I_load = Current for 80 scale divisions - shunt current
Finally, substitute the values into the equation and calculate the current through the load.