a 40.0 ohm resistor and a 90.0 ohm resistor are connected in parallel, and the combination is connected across a 120 V dc line. A)what is the resistance of the parallel combination. B)what is the total current through the parallel combination. C)what is the current through each resistor?
C) is perhaps the easiest part. Both of the two resistors have the full 120 V applied.
The current through the 40 ohm resistor is 120/40 = 3.0 A. The current through the 90 ohm resistor is
120/90 = 1.33 A
For B), just add the currents going through each resistor. 3.00 + 1.33 = ?
For A) you could divide the 120 V by the total current of B.
OR, you could use the formula 1/R = 1/40 + 1/90 = 9/360 + 4/360 = 13/360
R = 360/13
To solve this problem, we can use the formulas for resistors in parallel and Ohm's Law.
A) The formula for resistors in parallel is:
1/R_parallel = 1/R1 + 1/R2
where R_parallel represents the resistance of the parallel combination, and R1 and R2 are the resistances of the individual resistors.
Plugging in the given values:
1/R_parallel = 1/40.0 + 1/90.0
Calculating:
1/R_parallel = 0.025 + 0.0111
1/R_parallel = 0.0361
Taking the reciprocal of both sides:
R_parallel = 1 / 0.0361
R_parallel ≈ 27.6 ohms
Therefore, the resistance of the parallel combination is approximately 27.6 ohms.
B) According to Ohm's Law, the current through a circuit (I) can be calculated using the formula:
I = V / R
where I represents the current, V is the voltage, and R is the resistance.
Plugging in the given values:
I = 120 V / 27.6 ohms
Calculating:
I ≈ 4.35 A
Therefore, the total current through the parallel combination is approximately 4.35 Amperes.
C) Since the resistors are connected in parallel, the current through each resistor will be the same as the total current through the parallel combination. Therefore, the current through each resistor is also approximately 4.35 Amperes.
To solve this problem, we can use the formulas for resistance and current in parallel circuits.
A) To find the resistance of the parallel combination, we can use the formula:
1/R_total = 1/R1 + 1/R2 + ...
In this case, we have two resistors connected in parallel:
1/R_total = 1/R1 + 1/R2
Substitute the values given:
1/R_total = 1/40 + 1/90
Now, calculate the sum:
1/R_total = 0.025 + 0.0111
1/R_total = 0.0361
To find R_total, we take the reciprocal of 0.0361:
R_total = 1/0.0361
R_total ≈ 27.67 ohms
Therefore, the resistance of the parallel combination is approximately 27.67 ohms.
B) To find the total current through the parallel combination, we can use Ohm's Law. Ohm's Law states:
I = V/R
Where I is the current, V is the voltage, and R is the resistance.
In this case, the voltage is given as 120 V and the resistance is R_total = 27.67 ohms. Substitute these values into the formula:
I_total = 120 / 27.67
I_total ≈ 4.34 A
Therefore, the total current through the parallel combination is approximately 4.34 Amperes.
C) To find the current through each resistor, we can use the formula:
I_resistor = V / R
For the 40.0 ohm resistor:
I_40ohm = 120 / 40
I_40ohm = 3 A
For the 90.0 ohm resistor:
I_90ohm = 120 / 90
I_90ohm ≈ 1.33 A
Therefore, the current through the 40.0 ohm resistor is 3 Amperes, and the current through the 90.0 ohm resistor is approximately 1.33 Amperes.