Which of the following is a formula for calculating total resistance in a parallel circuit?

The correct answer is: 1 / Rt = 1 / R1 + 1 / R2 + ... + 1 / Rn

Where:

Rt is the total resistance of the parallel circuit

R1, R2, ..., Rn are the resistances of each individual resistor in the parallel circuit

To understand why this formula works, we can think about what happens when we connect resistors in parallel. When two resistors are connected in parallel, the current flowing through each resistor is the same. However, the voltage drop across each resistor is different. The voltage drop across a resistor is equal to the current flowing through the resistor multiplied by the resistance of the resistor. So, if we connect two resistors in parallel, the total current flowing through the circuit will be the same as the current flowing through each individual resistor. However, the total voltage drop across the circuit will be less than the voltage drop across each individual resistor. This is because the total resistance of the parallel circuit is less than the resistance of each individual resistor.

The formula for calculating total resistance in a parallel circuit can be derived by using Ohm's law. Ohm's law states that the current flowing through a resistor is equal to the voltage drop across the resistor divided by the resistance of the resistor. In a parallel circuit, the total current flowing through the circuit is the same as the current flowing through each individual resistor. So, we can write:

I = V / Rt

Where:

I is the total current flowing through the circuit

V is the total voltage drop across the circuit

Rt is the total resistance of the parallel circuit

We can also write:

I = V / R1

And:

I = V / R2

Where:

I is the current flowing through resistor 1

V is the voltage drop across resistor 1

R1 is the resistance of resistor 1

And:

I is the current flowing through resistor 2

V is the voltage drop across resistor 2

R2 is the resistance of resistor 2

Since the total current flowing through the circuit is the same as the current flowing through each individual resistor, we can equate the two equations:

V / Rt = V / R1 = V / R2

Rearranging, we get:

Rt = R1 * R2 / (R1 + R2)

This is the formula for calculating total resistance in a parallel circuit. It can be generalized to any number of resistors in parallel:

Rt = (1 / R1 + 1 / R2 + ... + 1 / Rn)

Where:

Rt is the total resistance of the parallel circuit

R1, R2, ..., Rn are the resistances of each individual resistor in the parallel circuit

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