A generator has a terminal voltage of 102V
when it delivers 10.3 A, and 92 V when it
delivers 31.9 A.
Calculate the emf.
Answer in units of V
Ri = (102-92)/(31.9-10.3) = 0.463 Ohms,
internal resistance.
E = 102 + 10.3*0.463 = 107 Volts.
Or E == 92 + 31.9*0.463 = 107 Volts.
To calculate the emf (electromotive force) of the generator, we can use the equation:
emf = terminal voltage + internal resistance × current
Let's calculate the internal resistance of the generator first. Using the two given points:
When delivering 10.3 A, the terminal voltage is 102 V
When delivering 31.9 A, the terminal voltage is 92 V
We can set up the following equations:
102 = emf + internal resistance × 10.3
92 = emf + internal resistance × 31.9
Now we have a system of two equations with two unknowns (emf and internal resistance). We can solve this system to find the values.
Let's solve it step-by-step using the method of substitution:
From the first equation, we can isolate emf:
emf = 102 - internal resistance × 10.3
Now substitute this expression for emf into the second equation:
92 = (102 - internal resistance × 10.3) + internal resistance × 31.9
Simplify the equation:
92 = 102 - 10.3 × internal resistance + 31.9 × internal resistance
Rearrange the terms:
92 = 102 + (31.9 - 10.3) × internal resistance
92 - 102 = 21.6 × internal resistance
-10 = 21.6 × internal resistance
Divide both sides by 21.6:
internal resistance = -10 / 21.6
internal resistance ≈ -0.463 V
Now we have the value of the internal resistance. Let's substitute this back into one of the initial equations to find the emf:
emf = 102 - (-0.463 × 10.3)
emf = 102 + 4.768
emf ≈ 106.768 V
Therefore, the emf of the generator is approximately 106.768 V.
To calculate the electromotive force (EMF) of the generator, we can use the equation:
EMF = terminal voltage + internal resistance * current
In this case, we have two data points with different currents and corresponding terminal voltages. We can use these values to determine the internal resistance and then calculate the EMF.
Let's denote:
V1 = Terminal voltage at current I1 = 102 V
V2 = Terminal voltage at current I2 = 92 V
I1 = 10.3 A
I2 = 31.9 A
First, we can calculate the internal resistance (r) using the formula:
r = (V1 - V2) / (I2 - I1)
Substituting the given values:
r = (102 V - 92 V) / (31.9 A - 10.3 A)
Now, let's calculate the internal resistance:
r = 10 V / 21.6 A
r ≈ 0.463 V/A
Next, we can calculate the EMF using the formula:
EMF = V1 + r * I1
Substituting the given values:
EMF = 102 V + 0.463 V/A * 10.3 A
Finally, let's calculate the EMF:
EMF ≈ 102 V + 4.76 V
EMF ≈ 106.76 V
Therefore, the electromotive force (EMF) of the generator is approximately 106.76 V.