What is the total resistance of a parallel circuit with resistances of 6 ohms, 14 ohms, 4 ohms, and 11 ohms?

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To find the total resistance in a parallel circuit, you use the formula for total resistance (R_total), which is given by:

1/R_total = 1/R1 + 1/R2 + 1/R3 + 1/R4

In this case, the resistances are 6 ohms, 14 ohms, 4 ohms, and 11 ohms.

First, calculate the reciprocal of each resistance:

1/6 = 0.1667

1/14 = 0.0714

1/4 = 0.2500

1/11 = 0.0909

Now, sum these values:

0.1667 + 0.0714 + 0.2500 + 0.0909 = 0.5790

Next, take the reciprocal of this sum to find R_total:

R_total = 1 / 0.5790 ≈ 1.73 ohms

This calculation confirms that the total resistance of the given resistances in parallel is approximately 1.73 ohms. Achieving a lower total resistance in a parallel circuit is due to the nature of how current can flow through multiple paths, which is why the formula results in