Which statement is correct about a parallel circuit?

Which statement is correct about a parallel circuit?

• A. Total resistance will be smaller than the smallest resistor.
• B. Total voltage drop is the same as the total resistance.
• C. Total resistance will decrease when one of the resistances is removed.
• D. The currents in each branch are equal.

Answer: (A)

In a parallel circuit, each resistor is connected across the same two points, so every branch has the same voltage source across it. Because each path provides a separate route for current, adding more parallel paths lowers the overall resistance the source sees. The equivalent resistance is found by 1/Req = sum(1/Ri), which makes Req smaller than any individual resistor, and indeed smaller than the smallest one. That’s why the statement about total resistance being smaller than the smallest resistor is the correct one. The total voltage drop across the network is the supply voltage and is the same across every branch; it isn’t a measure tied to the total resistance. If you remove a resistor from a parallel network, you reduce the number of current paths, so the overall resistance increases, not decreases. And currents in the branches depend on each branch’s resistance and only become equal if all branches have identical resistance.

In a parallel circuit, each resistor is connected across the same two points, so every branch has the same voltage source across it. Because each path provides a separate route for current, adding more parallel paths lowers the overall resistance the source sees. The equivalent resistance is found by 1/Req = sum(1/Ri), which makes Req smaller than any individual resistor, and indeed smaller than the smallest one. That’s why the statement about total resistance being smaller than the smallest resistor is the correct one.

The total voltage drop across the network is the supply voltage and is the same across every branch; it isn’t a measure tied to the total resistance. If you remove a resistor from a parallel network, you reduce the number of current paths, so the overall resistance increases, not decreases. And currents in the branches depend on each branch’s resistance and only become equal if all branches have identical resistance.