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?
To find the answers to these questions, we can use the formulas and principles of electrical circuits.
A) To determine the equivalent resistance in a parallel combination, we use the formula:
1/Requiv = 1/R1 + 1/R2 + ...
In this case, we can calculate the equivalent resistance using the formula:
1/Requiv = 1/40.0 + 1/90.0
Calculating this, we get:
1/Requiv = 0.025 + 0.0111
1/Requiv = 0.0361
Now, we can solve for Requiv by taking the reciprocal:
Requiv = 1 / 0.0361
Requiv ≈ 27.68 ohms
Therefore, the resistance of the parallel combination is approximately 27.68 ohms.
B) To find the total current through the parallel combination, we can use Ohm's Law, which states that:
I = V / R
Where I is the current, V is the voltage, and R is the resistance.
In this case, the voltage (V) is given as 120 V and the resistance (Requiv) we just found is 27.68 ohms.
So, substituting these values into the equation, we have:
I = 120 V / 27.68 ohms
Calculating this, we get:
I ≈ 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 fact that in a parallel combination, the voltage across each resistor is the same.
So, the current through each resistor can be determined using Ohm's Law:
I1 = V / R1
I2 = V / R2
Substituting the given values, we have:
I1 = 120 V / 40.0 ohms
I2 = 120 V / 90.0 ohms
Calculating these, we get:
I1 ≈ 3.00 A
I2 ≈ 1.33 A
Therefore, the current through the 40.0 ohm resistor is approximately 3.00 Amperes, and the current through the 90.0 ohm resistor is approximately 1.33 Amperes.