Connecting resistors in parallel

In summary, when resistors are connected in parallel, the voltage is the same through all branches and the current is inversely proportional to the resistance. This means that the resistor with the larger value will carry a smaller proportion of the current. However, impedance, which includes both resistance and reactance, must be taken into account when calculating the total current in a parallel circuit.
  • #1
mich_v87
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When resistors are connected in parallel, which one , according to resistance value, carries the larger proportion of the currents? Does the ratio appear to be directly, or inversely, proportional to the ratio of the resistances?
 
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  • #2
Note that resistance is a type of impedance but that impedance is not necessarily just resistance but something that comes up with AC called reactance or both.

When devices are placed in parallel, voltage is the same through all branches (unless a capacitor is in one branch) and charge (and therefore current) is inversely proportional.

So for example, two resistors in parallel are 10k and 5k. Total impedance is approx 3.33k. Voltage into the parallel node is 10V. Thus total current is 10V/3.33k or about 3mA. Solve for current along each branch with current divider and you will find 2mA along the 5k branch and 1 mA along the 10k branch.
 
  • #3


When resistors are connected in parallel, the one with the lower resistance value will carry a larger proportion of the current. This is because in a parallel circuit, the total resistance decreases as more resistors are added. Therefore, the resistor with the lower resistance will have a larger share of the total current.

The ratio of the currents is inversely proportional to the ratio of the resistances. This means that as the resistance ratio increases, the current ratio decreases. This can be explained by Ohm's Law, which states that the current flowing through a conductor is directly proportional to the voltage and inversely proportional to the resistance. In this case, the voltage across each resistor is the same, but the resistance decreases as more resistors are added in parallel, resulting in an increase in current.
 

1. How do you calculate the equivalent resistance of resistors connected in parallel?

The equivalent resistance of resistors connected in parallel can be calculated using 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. Once you have calculated the sum of the reciprocals, take the reciprocal of that value to get the equivalent resistance.

2. What is the purpose of connecting resistors in parallel?

Connecting resistors in parallel allows for the current to divide and flow through each resistor separately, resulting in a decrease in the overall resistance of the circuit. This can be useful in cases where you need to lower the resistance in a circuit or distribute the current evenly among multiple components.

3. How does the voltage change when resistors are connected in parallel?

The voltage across each resistor in a parallel circuit will be the same as the voltage across the whole circuit. This means that the voltage does not change when resistors are connected in parallel.

4. Can resistors with different values be connected in parallel?

Yes, resistors with different values can be connected in parallel. However, it is important to note that the equivalent resistance will be lower than the lowest individual resistance. This is due to the fact that the current will flow through the path of least resistance and thus, the resistor with the lowest value will have the most current flowing through it.

5. What happens to the total power dissipated when resistors are connected in parallel?

The total power dissipated in a parallel circuit is equal to the sum of the power dissipated in each individual resistor. This means that the total power dissipated increases as more resistors are added in parallel.

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