Three resistors A, B, and Care connected in series to a 117-volt source, If Ra = 64 ohms, and E = 40 volts when the current is 0.5 amp, calculate the resistances Re and Rc.
E is from where to where ?
To calculate the resistances Re and Rc, we need to use the formulas for calculating resistance and voltage in a series circuit. Here are the steps:
Step 1: Calculate the total resistance (Rt) in the series circuit.
In a series circuit, the total resistance is the sum of the individual resistances:
Rt = Ra + Rb + Rc
Step 2: Calculate the total current (It) in the circuit.
Since the resistors are connected in series, the current passing through each resistor is the same.
It = 0.5 Amps (given)
Step 3: Calculate the total voltage (Vt) across the series circuit.
Vt = 117 volts (given)
Step 4: Calculate the voltage drop across each resistor.
The voltage drop across each resistor can be calculated using Ohm's law:
Voltage drop = Resistance × Current
For resistor A (Ra):
Voltage drop across Ra (Ea) = Ra × It
For resistor B (Rb):
Voltage drop across Rb (Eb) = Rb × It (since no specific value is given, we will use this formula in the next step)
For resistor C (Rc):
Voltage drop across Rc (Ec) = Rc × It
Step 5: Calculate the resistance Re.
Given that the voltage across Re is 40 volts and the current is 0.5 Amps, we can use Ohm's law to find the resistance:
Re = Voltage drop across Re / Current
Re = 40 volts / 0.5 Amps
Step 6: Calculate the resistance Rc.
To find Rc, we need to subtract the values of Ra (64 ohms) and Re from the total resistance (Rt):
Rc = Rt - Ra - Re
Now, let's plug in the given values and calculate the resistances:
Step 1: Calculate the total resistance (Rt):
Rt = Ra + Rb + Rc
Step 2: Calculate the total current (It):
It = 0.5 Amps
Step 3: Calculate the total voltage (Vt):
Vt = 117 volts
Step 4: Calculate the voltage drop across each resistor:
Since no specific value is given for Rb, we cannot calculate the voltage drop specifically across Rb.
Step 5: Calculate the resistance Re:
Re = 40 volts / 0.5 Amps
Step 6: Calculate the resistance Rc:
Rc = Rt - Ra - Re
By following these steps and plugging in the given values, you will be able to calculate the resistances Re and Rc.