A series-wound dc motor has an internal resistance of 6 W. The 120-V supply line draws 8 A when at full speed. What is the emf in the motor and the starting current?
To find the emf in the motor and the starting current, we need to use the formulas for series-wound dc motors.
1. The emf in the motor (E) can be calculated using Ohm's Law, which relates the voltage (V), current (I), and resistance (R) in a circuit. The formula is E = V - IR, where E is the emf, V is the supply line voltage, I is the current, and R is the internal resistance of the motor.
2. Starting current (I_start) can be calculated by dividing the supply line voltage (V) by the sum of the motor's internal resistance (R) and the resistance of the external circuit (R_ext). The formula is I_start = V / (R + R_ext).
Now let's solve the problem step by step.
Given:
- Internal resistance (R) = 6 Ω
- Supply line voltage (V) = 120 V
- Current at full speed (I) = 8 A
1. Emf in the motor (E):
Using the formula E = V - IR, we can substitute the given values:
E = 120 V - (8 A * 6 Ω)
E = 120 V - 48 V
E = 72 V
So, the emf in the motor is 72 V.
2. Starting current (I_start):
We need to know the resistance of the external circuit (R_ext) to calculate the starting current. If the problem doesn't provide that information, it's not possible to calculate the exact starting current without further details.
However, if we assume that there is no external resistance (R_ext = 0), we can use the formula I_start = V / (R + R_ext) and substitute the given values:
I_start = 120 V / (6 Ω + 0 Ω)
I_start = 120 V / 6 Ω
I_start = 20 A
In this case, if there is no external resistance, the starting current would be 20 A.
Remember that these calculations assume the absence of an external resistance. If there is any external resistance, please provide that information for a more accurate result.