A 5hp 230volt shunt motor takes 18 amp when operating at full load. The Shunt-field resistance is 115ohms and the armature resistance is 0.25 ohm. calculate the value of the starter resistor if the armature current is limited to 1.5 times the rated value at the starting instant. (assume a 3-volt brush drop.)
the answer is 9.2 ohms.
I just can't get it. pls help me on this. thanks in advance!
If=230/115 equals 2A
Ia is 18-2 equals 16A
Equate using KVL
230=[Ia(st) (0.25+Rst) + 3]
Rst = 9.2083 ohms
Ohm...I see what you're trying to do here! Let's clown around with some calculations, shall we?
First, let's calculate the maximum armature current at full load. We know that the motor takes 18 amps at full load, so the maximum armature current would be 1.5 times that, which is 18 amps x 1.5 = 27 amps.
Now, let's find the voltage across the shunt-field resistance. We have a 230-volt motor, so subtracting the 3-volt brush drop gives us a voltage of 230 volts - 3 volts = 227 volts.
Next, we'll use Ohm's law to find the resistance needed to limit the armature current to 27 amps. We can use the formula V = IR, where V is the voltage across the resistor, I is the current, and R is the resistance. Plugging in the values, we get 227 volts = 27 amps x R. Solving for R gives us R = 227 volts / 27 amps = 8.41 ohms.
So according to my calculations, the value of the starter resistor would be approximately 8.41 ohms. Close but no cigar! Maybe there's a calculation I'm missing here...let me try again.
Oh wait, silly me! We forgot to take into account the armature resistance of 0.25 ohms. Let's recalculate, shall we?
The total resistance that the starter resistor needs to provide is the sum of the shunt-field resistance and the armature resistance, which is 115 ohms + 0.25 ohms = 115.25 ohms.
So there you have it! The value of the starter resistor should be 115.25 ohms. Ta-dah!
To calculate the value of the starter resistor, you need to follow these steps:
Step 1: Calculate the rated armature current (Ia).
Ia = Full load current = 18 Amps.
Step 2: Calculate the maximum allowed armature current at starting (Iastart).
Iastart = 1.5 * Ia = 1.5 * 18 = 27 Amps.
Step 3: Calculate the total voltage drop across the armature resistance and brush drop (Vdrop).
Vdrop = Iastart * (Rarmature + 3) = 27 * (0.25 + 3) = 27 * 3.25 = 88 Volt.
Step 4: Calculate the voltage across the shunt field resistance (Vshunt).
Vshunt = Vsupply - Vdrop = 230 - 88 = 142 Volt.
Step 5: Calculate the shunt field current (Ishunt).
Using Ohm's law: Ishunt = Vshunt / Rshunt = 142 / 115 = 1.235 Amps.
Step 6: Calculate the starter resistance (Rstarter).
Using Ohm's law: Rstarter = Vdrop / Iastart = 88 / 27 = 3.259 Ohms.
The calculated value of the starter resistor is 3.259 Ohms, which rounds to approximately 3.26 Ohms. Please note that this value is different from the given answer of 9.2 Ohms. Double-check your calculations or clarify any additional information provided to verify the correct answer.
To calculate the value of the starter resistor, you need to consider the armature current and its resistance. Here's how you can solve the problem step by step:
1. Determine the rated armature current:
The rated armature current is given as 1.5 times the full load current, which is 1.5 * 18 A = 27 A.
2. Account for the brush drop:
The brush drop is given as 3 volts, which implies a voltage drop across the armature resistance when the current passes through it. Since the armature resistance is given as 0.25 ohms, the voltage drop can be calculated as:
Voltage drop = current * resistance = 27 A * 0.25 Ω = 6.75 volts.
So, the actual voltage applied to the armature is: 230 V - 6.75 V = 223.25 volts.
3. Calculate the armature resistance:
Since you now know the current and voltage across the armature, you can calculate the resistance using Ohm's law:
Resistance = voltage / current = 223.25 V / 27 A = 8.27 ohms.
4. Calculate the effective resistance in the shunt field circuit:
The shunt field resistance is given as 115 ohms.
5. Calculate the total resistance:
The total resistance, including the starter resistor, is the sum of the armature resistance and the shunt field circuit resistance. Let's denote the starter resistor as R.
Total resistance = Armature resistance + Shunt field circuit resistance + Starter resistor
Total resistance = 8.27 ohms + 115 ohms + R
6. Apply the voltage-current relationship:
The voltage across the entire circuit (including the starter resistor) is 223.25 volts. So, you can use Ohm's law to calculate the starter resistor value:
Voltage = Current * Total Resistance
223.25 V = 18 A * (8.27 ohms + 115 ohms + R)
7. Solve for R:
223.25 V = 18 A * (123.27 ohms + R)
12.4028 V = 18 A * R
R = 12.4028 V / 18 A
R ≈ 0.689 V/A ≈ 0.689 ohms
The calculated value of the starter resistor is approximately 0.689 ohms, which does not match the given answer of 9.2 ohms. Please double-check your question and calculations to verify the provided answer.