In a circuit with two parallel branches of equal resistance connected to the same source, how do the branch currents compare?

In a circuit with two parallel branches of equal resistance connected to the same source, how do the branch currents compare?

• A. Each branch carries the same current; the total current is the sum of the branch currents.
• B. One branch carries all the current.
• C. Currents cancel each other out.
• D. Total current equals the current in a single branch.

Answer: (A)

In a parallel circuit, the voltage across each branch is the same. When both branches have the same resistance, the current through each branch must be the same because I = V/R and V is identical for both paths while R is identical as well. So each branch carries the same current. The total current drawn from the source is the sum of the branch currents, which, for two equal branches, is twice the current in one branch (I_total = 2 × I_branch). Currents don’t cancel in parallel; they simply split and then recombine, and with equal resistances they split equally. For example, if the voltage across each branch is V and each branch resistance is R, each branch current is V/R and the total current is 2V/R.

In a parallel circuit, the voltage across each branch is the same. When both branches have the same resistance, the current through each branch must be the same because I = V/R and V is identical for both paths while R is identical as well. So each branch carries the same current. The total current drawn from the source is the sum of the branch currents, which, for two equal branches, is twice the current in one branch (I_total = 2 × I_branch). Currents don’t cancel in parallel; they simply split and then recombine, and with equal resistances they split equally. For example, if the voltage across each branch is V and each branch resistance is R, each branch current is V/R and the total current is 2V/R.