Connecting resistors in parallel

[mich_v87]

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?

 

[thtadthtshldntbe]

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.

 

[quicknote]

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.