Question

Can all of the currents going into the junction in figure below be positive? Explain.

Short answer

At least one of the currents flowing through a junction should be negative.

Step-by-step solution

Kirchhoff's first law

Kirchhoff's first law states that, in a circuit, the sum of currents flowing towards a particular junction should be equal to the sum of currents flowing away from that junction.

Step 2:

According to Kirchhoff's first law, the sum of currents flowing through a junction has to be zero. If we have three currents\({I_1}\),\({I_2}\)and\({I_3}\), then-

\[\begin{array}{l}{I_1} + {I_2} + {I_3} = 0\\{I_1} + {I_2} = - {I_3}\end{array}\]

From the above relation, it is clear that at least one of the currents should be negative, then only the sum of currents will be zero.

Thus, all the currents flowing through the junction cannot be positive.