In a parallel circuit, how do you find the total resistance?

In a parallel circuit, the total resistance is calculated by adding the inverses of each individual resistance value. The reason for this approach is rooted in how voltage and current operate in parallel configurations. In a parallel circuit, each component is connected directly to the voltage source, meaning that the voltage across each resistor is the same.

When resistors are connected in parallel, the total current flowing through the circuit is the sum of the currents flowing through each individual resistor. The relationship between voltage (V), current (I), and resistance (R) in a resistor is described by Ohm's law (V = I × R). Since voltage is constant across all resistors in a parallel circuit, the total current (I_total) can be defined as:

I_total = I_1 + I_2 + I_3 + ...

Where each I represents the current through each resistor. Using Ohm's law to express each current in terms of resistance gives:

I_1 = V / R_1,

I_2 = V / R_2,

I_3 = V / R_3,

This leads to the equation for total current:

I_total = V / R_total,

Combining these relationships, we find:

V / R_total =