In a circuit containing a 10 Ω resistor in parallel with a 10 Ω resistor, what is the current ratio if the same voltage is across both?

In a circuit containing a 10 Ω resistor in parallel with a 10 Ω resistor, what is the current ratio if the same voltage is across both?

• A. The currents are unequal and depend on the supply only.
• B. The currents are equal; the total current is twice the current through one resistor.
• C. The current through each resistor is half the total current.
• D. The total current is the sum of the two currents.

Answer: (B)

In a parallel circuit, the same voltage is across every branch, and the current through each branch depends on that branch’s resistance (I = V/R). If the resistors have equal resistance, the currents through each branch are the same. Here, both resistors are 10 Ω, so each branch draws I = V/10. That means the two branch currents are equal, giving a current ratio of 1:1. The total current is the sum of the branch currents: Itot = I1 + I2 = V/10 + V/10 = V/5, which is twice the current through one resistor. So the statement that the currents are equal and the total current is twice the current through one resistor correctly describes the situation.

In a parallel circuit, the same voltage is across every branch, and the current through each branch depends on that branch’s resistance (I = V/R). If the resistors have equal resistance, the currents through each branch are the same. Here, both resistors are 10 Ω, so each branch draws I = V/10. That means the two branch currents are equal, giving a current ratio of 1:1.

The total current is the sum of the branch currents: Itot = I1 + I2 = V/10 + V/10 = V/5, which is twice the current through one resistor. So the statement that the currents are equal and the total current is twice the current through one resistor correctly describes the situation.