TWO RESISTORS, 3 OHMS AND 18 OHMS , ARE IN PARALLEL AND THIS COMBINATION IS CONNECTED IN SERIES TO ANOTHER PARALLEL GROUP OF 2, 4, AND 12 OHMS
A.) FIND THE JOINT RESISTANCE OF THE GROUP
B.) FIND THE CURRENT THROUGH EACH RESISTOR IF THE CURRENT THROUGH EACH RESISTOR IF THE CURRENT THROUGH THE WHOLE GROUP IS AMPARES.
To solve this problem, we need to follow a few steps:
Step 1: Find the equivalent resistance for each parallel group.
Step 2: Combine the equivalent resistances from each parallel group in series.
Step 3: Use Ohm's Law to calculate the current through each resistor.
Let's go through each step.
Step 1: Finding the equivalent resistance for each parallel group
For the first parallel group with resistors of 3 ohms and 18 ohms, we can use the formula for calculating the equivalent resistance of two resistors in parallel:
1/Req = 1/R1 + 1/R2
where Req is the equivalent resistance and R1, R2 are the resistances of the individual resistors.
Plugging in the values:
1/Req = 1/3 + 1/18
Simplifying:
1/Req = (6 + 1)/18
1/Req = 7/18
Taking the reciprocal:
Req = 18/7 ohms or approximately 2.57 ohms.
For the second parallel group with resistors of 2 ohms, 4 ohms, and 12 ohms, we can use the same formula:
1/Req = 1/R1 + 1/R2 + 1/R3
Plugging in the values:
1/Req = 1/2 + 1/4 + 1/12
Simplifying:
1/Req = (6 + 3 + 1)/12
1/Req = 10/12
Taking the reciprocal:
Req = 12/10 ohms or 1.2 ohms.
Step 2: Combining the equivalent resistances from each parallel group in series
Since the two groups are connected in series, the equivalent resistance of the whole group is the sum of the equivalent resistances of each group:
Rtotal = Req1 + Req2
Rtotal = 2.57 + 1.2
Rtotal = 3.77 ohms.
So, the joint resistance of the group is approximately 3.77 ohms.
Step 3: Calculating the current through each resistor
Now that we have the joint resistance, we can use Ohm's Law to calculate the current through each resistor. Ohm's Law states that:
I = V/R
where I is the current, V is the voltage, and R is the resistance.
Since the question doesn't provide the voltage, we'll assume it to be 1 volt for simplicity. Therefore, the current through the whole group is 1 ampere.
For each resistor, the current can be calculated using:
I = V/R
I1 = 1/3.77 ≈ 0.265 amperes (or 265 milliamperes)
I2 = 1/3.77 ≈ 0.265 amperes
I3 = 1/3.77 ≈ 0.265 amperes
I4 = 1/3.77 ≈ 0.265 amperes
I5 = 1/3.77 ≈ 0.265 amperes
I6 = 1/3.77 ≈ 0.265 amperes
Therefore, the current through each resistor is approximately 0.265 amperes (or 265 milliamperes).