How to find the current and equivalent resistance in a parallel circuit

In summary, for a parallel circuit with three 16 ohm resistors connected to a 34 V battery, the equivalent resistance is 3/16 ohms and the current delivered by the battery is 0.7917 amps. To find the equivalent resistance, the formula (1/equivalent resistance) = 1/R1+1/R2+1/R3+... is used and the inverse of the result is taken. To find the current, the formula I=V/R is used with the equivalent resistance found in part a).
  • #1
itsmarasilly
24
0

Homework Statement



Three 16 ohm resistors are connected in parallel and placed across a 34 V battery.
(a) What is the equivalent resistance of the parallel circuit?
(b) What is the current delivered by the battery?

Homework Equations



(a) (1/equivalent resistance) = 1/R1+1/R2+1/R3+...
(b) I=V/R

The Attempt at a Solution



(a) (1/16)+(1/16)+(1/16) = (3/16)
equivalent resistance = (3/16)
(b) (34 V / 48 ohm) = .7917 amps
 
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  • #2
For resistors in parallel we have that:

[tex]
1/R_{total} = 1/R_1+1/R_2+1/R_3 + \ldots,
[/tex]

so you need to take the inverse of the result you gave.

For (b), use the answer from (a) and the expression you correctly wrote: I = V/R.
 
  • #3
Compare your a) relevant equation to your a) solution attempt. There is something very simple missing.

b) You must find the correct resistance in part a) to solve.

Edit- Niles beat me
 

1. How do you calculate the total current in a parallel circuit?

In a parallel circuit, the total current is equal to the sum of the individual branch currents. This means that you can find the total current by adding up the currents in each branch of the circuit.

2. How do you find the equivalent resistance in a parallel circuit?

To find the equivalent resistance in a parallel circuit, you can use the formula: 1/Req = 1/R1 + 1/R2 + 1/R3 + ... + 1/Rn, where Req is the equivalent resistance and R1, R2, R3, etc. are the individual resistances in each branch. Once you have this value, you can use Ohm's Law (V = IR) to find the current in the circuit.

3. Can the equivalent resistance in a parallel circuit ever be lower than the individual resistances?

Yes, the equivalent resistance in a parallel circuit can be lower than the individual resistances. This is because in a parallel circuit, the total current is divided between the branches, which means that the individual resistances are experiencing less current than if they were in a series circuit. This results in a lower equivalent resistance.

4. How does the number of branches in a parallel circuit affect the equivalent resistance?

The more branches there are in a parallel circuit, the lower the equivalent resistance will be. This is because adding more branches creates more paths for the current to flow through, reducing the overall resistance in the circuit. As a result, the equivalent resistance decreases as the number of branches increases in a parallel circuit.

5. How do you calculate the current in each branch of a parallel circuit?

To calculate the current in each branch of a parallel circuit, you can use Ohm's Law (V = IR) along with the total current and the individual resistances in each branch. Simply rearrange the formula to solve for the current (I = V/R) and plug in the appropriate values for each branch to find the current in that specific branch.

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