suppose you had a circuit with three resistors in series and you measured I=7.0 milliamps; V = 14.7 volts; V1= 3.5 volts and V2 = 1.4 volts. What would be the voltage across the third resistor? What would its resistance be?
I = 7.0 mA
V = 14.7 Volts.
v1 = 3.5 Volts.
V2 = 1.4 Volts.
a. V3 = V-V1-V2
b. R3 = V3/I
I = 0.007 Amps
To find the voltage across the third resistor (V3), we can use Ohm's law:
V = I * R
In this case, the measured current (I) is 7.0 milliamps, and the total voltage (V) is 14.7 volts. Since the resistors are connected in series, the total voltage is the sum of the individual voltage drops across each resistor:
V = V1 + V2 + V3
Substituting the given values:
14.7 volts = 3.5 volts + 1.4 volts + V3
Simplifying the equation:
V3 = 14.7 volts - 3.5 volts - 1.4 volts
V3 = 9.8 volts
Therefore, the voltage across the third resistor (V3) would be 9.8 volts.
Now, to find the resistance of the third resistor (R3), we can rearrange Ohm's law:
R = V / I
Substituting the given values:
R3 = V3 / I
R3 = 9.8 volts / 7.0 milliamps
To ensure consistent units, we need to convert milliamps to amps:
R3 = 9.8 volts / (7.0 * 10^-3 amps)
R3 ≈ 1,400 ohms
Therefore, the resistance of the third resistor (R3) would be approximately 1,400 ohms.
To find the voltage across the third resistor and its resistance, we need to use Ohm's Law and the concept of voltage division in a series circuit.
In a series circuit, the total voltage across all the resistors is equal to the sum of the voltages across each individual resistor. So, the total voltage (V) in this case is 14.7 volts, which is equal to the sum of V1, V2, and the voltage across the third resistor (V3).
V = V1 + V2 + V3
Now, we know that V1 is 3.5 volts and V2 is 1.4 volts. Therefore, we can rearrange the equation to solve for V3:
V3 = V - (V1 + V2)
= 14.7 V - (3.5 V + 1.4 V)
= 14.7 V - 4.9 V
= 9.8 V
So, the voltage across the third resistor (V3) is 9.8 volts.
To find the resistance of the third resistor, we can use Ohm's Law:
V = I * R
Where:
V is the voltage across the resistor,
I is the current flowing through the resistor,
R is the resistance of the resistor.
In this case, we know that I (current) is 7.0 milliamps (mA) and V (voltage) is 9.8 volts. We can rearrange the equation to find the resistance (R):
R = V / I
= (9.8 V) / (7.0 mA)
≈ 1.4 kΩ (kilo-ohms)
Therefore, the resistance of the third resistor is approximately 1.4 kilo-ohms.