Parallel Circuits

A parallel circuit can now be established by connecting a supply across a set of parallel resistors as shown in Fig. 1. The positive terminal of the supply is directly connected to the top of each resistor, while the negative terminal is connected to the bottom of each resistor. Therefore, it should be quite clear that the applied voltage is the same across each resistor. In general, Therefore, remember that For the voltages of the circuit in Fig. 1, the result is that Once the supply has been connected, a source current is established through the supply that passes through the parallel resistors. The smaller the total resistance, the greater is the current, as occurred for series circuits also. The source current can then be determined using Ohm's law: Since the voltage is the same across parallel elements, the current through each resistor can also be determined using Ohm's law. That is, The direction for the currents is dictated by the polarity of the voltage across the resistors. Recall that for a resistor, current enters the positive side of a potential drop and leaves the negative side. The result, as shown in Fig. 1, is that the source current enters point a, and currents $I_1$ and $I_2$ leave the same point. But $ E = V_1 = V_2$