In a parallel circuit, adding another identical resistor reduces the total resistance. Which statement is true?

In a parallel circuit, adding another identical resistor reduces the total resistance. Which statement is true?

• A. The total resistance decreases
• B. The total resistance increases
• C. The total resistance stays the same
• D. The total resistance becomes infinite

Answer: (A)

In parallel circuits, adding more paths for current lowers the total resistance. This happens because the conductance (the reciprocal of resistance) adds up when resistors share the same voltage. For identical resistors, the equivalent resistance becomes R/n, where n is how many resistors are in parallel. So adding one more identical resistor changes R to R/(n+1), which is smaller. For example, two identical resistors of 100 ohms in parallel give 50 ohms, and three give about 33.3 ohms. The voltage across each resistor is the same, but the total current the source must supply increases as more current can flow through the additional path. This is why the total resistance decreases, and it definitely does not increase, stay the same, or become infinite.

In parallel circuits, adding more paths for current lowers the total resistance. This happens because the conductance (the reciprocal of resistance) adds up when resistors share the same voltage. For identical resistors, the equivalent resistance becomes R/n, where n is how many resistors are in parallel. So adding one more identical resistor changes R to R/(n+1), which is smaller.

For example, two identical resistors of 100 ohms in parallel give 50 ohms, and three give about 33.3 ohms. The voltage across each resistor is the same, but the total current the source must supply increases as more current can flow through the additional path. This is why the total resistance decreases, and it definitely does not increase, stay the same, or become infinite.