The parallel resistance derivation is used for how many resistors in parallel?

The parallel resistance derivation is used for how many resistors in parallel?

• A. Two
• B. Three
• C. Four
• D. Any number

Answer: (A)

In parallel circuits, the total resistance is found by combining the conductances of all branches. The voltage across every resistor in parallel is the same, and the currents through the branches add up to the total current. If you write the current in each branch as Ii = V/Ri and sum them, you get Itot = V(1/R1 + 1/R2 + ... + 1/Rn). The equivalent resistance then becomes Req = V/Itot = 1 / (1/R1 + 1/R2 + ... + 1/Rn). This expression works for any number of resistors in parallel—two, three, four, or more. The two-resistor case is simply the simplest example; you can extend the same derivation to include more resistors, and the same form remains.

In parallel circuits, the total resistance is found by combining the conductances of all branches. The voltage across every resistor in parallel is the same, and the currents through the branches add up to the total current. If you write the current in each branch as Ii = V/Ri and sum them, you get Itot = V(1/R1 + 1/R2 + ... + 1/Rn). The equivalent resistance then becomes Req = V/Itot = 1 / (1/R1 + 1/R2 + ... + 1/Rn). This expression works for any number of resistors in parallel—two, three, four, or more. The two-resistor case is simply the simplest example; you can extend the same derivation to include more resistors, and the same form remains.