In a parallel circuit, what happens to the total resistance when more branches are added, with a constant supply?

In a parallel circuit, what happens to the total resistance when more branches are added, with a constant supply?

• A. It increases
• B. It stays the same
• C. It decreases
• D. It becomes infinite

Answer: (C)

In a parallel circuit, adding more branches creates additional pathways for current to flow. The total resistance is found from the reciprocal sum of each branch: 1/Req = 1/R1 + 1/R2 + ... . When you add another branch with resistance Rn, you add 1/Rn to that sum, which increases the total conductance and forces Req to become smaller. So the overall resistance drops as more parallel paths are added. With a constant supply voltage, the current increases accordingly because I = V/Req. For example, two identical resistors R in parallel give Req = R/2, and three identical resistors R give Req = R/3. If a branch is open (infinite resistance), it doesn’t affect the total; but as long as there are additional conducting branches, the total resistance decreases.

In a parallel circuit, adding more branches creates additional pathways for current to flow. The total resistance is found from the reciprocal sum of each branch: 1/Req = 1/R1 + 1/R2 + ... . When you add another branch with resistance Rn, you add 1/Rn to that sum, which increases the total conductance and forces Req to become smaller. So the overall resistance drops as more parallel paths are added. With a constant supply voltage, the current increases accordingly because I = V/Req.

For example, two identical resistors R in parallel give Req = R/2, and three identical resistors R give Req = R/3. If a branch is open (infinite resistance), it doesn’t affect the total; but as long as there are additional conducting branches, the total resistance decreases.