@ElektrodaBot If I have a DC circuit with a 10 volt supply followed by a 10 ohm resistor, leading to a 27 ohm and a 28 ohm resistor in parallel, what is the voltage across each resistor in the circuit?
If I have a DC circuit with a 10 volt supply followed by a 10 ohm resistor, leading to a 27 ohm and a 28 ohm resistor in parallel, what is the voltage across each resistor in the circuit?
To find the voltage across each resistor, we'll first have to determine the equivalent resistance of the parallel combination of the 27 ohm and 28 ohm resistors, and then use Ohm's law and the voltage divider rule to find the voltages.
1. Calculate the equivalent resistance of the parallel resistors: 1/R_parallel = 1/27 + 1/28 R_parallel = 13.86 ohms (approximately)
2. Calculate the total resistance in the circuit: R_total = 10 ohms (the first resistor) + 13.86 ohms (the parallel combination) R_total = 23.86 ohms
3. Calculate the total current in the circuit using Ohm's law: I = V/R I = 10V / 23.86 ohms I = 0.419 A (approximately)
4. Calculate the voltage across the 10 ohm resistor using Ohm's law: V_10ohm = I * R V_10ohm = 0.419 A * 10 ohms V_10ohm = 4.19 V (approximately)
5. Calculate the voltage across the parallel combination of the 27 ohm and 28 ohm resistors: Since the resistors are in series, the voltage across the parallel combination will be equal to the remaining voltage in the circuit: V_parallel = 10V (supply voltage) - 4.19 V (voltage across 10 ohm resistor) V_parallel = 5.81 V (approximately)
So, the voltage across the 10 ohm resistor is approximately 4.19 V, and the voltage across both the 27 ohm and 28 ohm resistors (in parallel) is approximately 5.81 V.
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I think the translation is wrong. It should be "then a 10 ohm resistor, leading to a 27 ohm resistor and a 28 ohm resistor, connected in parallel". Or ''then a 10 ohm resistor going parallel to a 27 ohm resistor and a 28 ohm resistor'' where the word in parallel should be understood as simultaneously . The most common synonyms of the word parallel are: at the same time, at the same time, at the same time, at the same time...
In the case of a 10 V voltage source loaded with resistors connected in PARALLEL (regardless of their value), the voltage drop across each resistor will be 10 V.
What will be different for each of the resistors is the CURRENT flowing through the individual resistors.
A simple relationship works here: U = I * R.
that is: I = U/R
U will be 10 V each time, so: - for a 10 ohm resistor: I = 10 V/10 ohm = 1 A; - for a 27 ohm resistor: I = 10 V/27 ohm = 370 mA; - for a 28 ohm resistor: I = 10 V/28 ohm = 357 mA.
The total current loading the voltage source is the sum of the currents flowing through the above-mentioned resistors, i.e. I = 1.727 A.
The total equivalent resistance can be calculated in two ways. one is: 1/Rz = 1/R1 + 1/R2 + 1/R3 That is: 1/Rz = 1/10 + 1/27 + 1/28 [1/ohm]
but with the total current it is probably easier to use U = I * R -> Rz = U/I, i.e. Rz = 10 V/1.727 A = 5.79 ohms.
Oh my, so there's a voltage source in series with R = 10 ohms, then 27 ohms and 28 ohms connected in parallel.
Again, the task is child's play. At 27 ohm and 28 ohm, the voltage drop is the same - it's best to make an equivalent resistance here:
1/Rz = 1/27 + 1/28 [1/ohm] -> Rz = 13.75 ohm
At this point, there are two resistors in series: R1 = 10 ohm and Rz = 13.75 ohm.
Rtotal = 10 ohms + 13.75 ohms = 23.75 ohms
From the relationship U = I*R we have the current (common for the entire circuit): I = 10 V/23.75 ohm = 0.421 A
So the voltage drop across R1 is U = 0.412A * 10 ohm = 4.12V. The voltage drop on R2 and R3 is identical because they are connected in parallel: U = 0.412 A * 13.75 ohm = 5.78 V, which can also be calculated more simply: 10 V - 4.12 V = 5.78 V.
If you want to count the currents through R2 and R3, you go back to U = I*R -> I = U/R again
Replace U with 5.78 V, replace R with R2 = 27 ohms and R3 = 28 ohms.
The link to calculating equivalent resistances is still valid - it is well described and worth reading, if only to understand ...
A diagram of the circuit would have clarified the question more but still taking your question in assumption we have 3 resistors with DC input of 10V and we want to find the voltage across resistors.
First of all we need to find the equivalent resistances of the circuit in this way;
This formula will be used for parallel 2 resistors : 1\R4=1\R2 + 1\R3
1\R4 =1\27 + 1\28
R4 = 13.7 ohms.
This formula will be used for R1 and R4 resistors: Req = R3 + R4
Req=10+13.7
Req = 23.7 ohms.
Now we find the current I in the circuit;
I=V\R
I=10\23.7
I=0.421 Amp.
The voltage drop across 10 ohm resistors is;
V2=I x R1
V2=0.421 x 10
V2=4.21 volts.
The voltage drop across parallel 28 and 27 ohm resistors will be same that is;
V3=I x R4
V3=0.421 x 13.7
V3=5.76 volts.
Finally, the voltage across the 10 ohm resistor is 4.21 volts, and the voltage across both the 27 ohm and 28 ohm resistors (in parallel) is 5.76 volts.
In a DC circuit with a 10V supply, a 10 ohm resistor is in series with a parallel combination of 27 ohm and 28 ohm resistors. To determine the voltage across each resistor, the equivalent resistance of the parallel resistors is calculated as approximately 13.75 ohms. The total resistance in the circuit is then 23.75 ohms, leading to a total current of approximately 0.421 A. The voltage drop across the 10 ohm resistor is approximately 4.21 V, while the voltage across the parallel combination of the 27 ohm and 28 ohm resistors is approximately 5.79 V. The current through each parallel resistor can be calculated using Ohm's law, resulting in different current values for each resistor. Summary generated by the language model.
