Current sources. An ideal current source is a circuit element that is complementary to a battery. An ideal battery maintains a constant voltage across its terminals. The current that flows in the battery is determined by the details of the circuit to which the battery is connected. An ideal current source supplies a definite current. The voltage across the terminals of the current source is determined by the details of the circuit to which it is connected. The symbol for a current source is a circle with an arrow inside. The direction of the arrow indicates the direction in which the current flows through the current source. *
(a) One loop analysis. The current through the resistor R must be i the same as the current supplied by the current source. Let V be the (at present unknown) voltage across the current source. Then according to Kirchoff's loop law V – iR = 0. This leads to the result V = iR.
(b) Two loop analysis. In principle there are five unknowns: the currents 11, 12 and iz and the voltages VA and VB across the two current sources. We wish to determine these quantities in terms of the presumed known values of the three resistors R1, R2 and R3 and the currents i A and is supplied by the two sources.
(i) Current analysis. Evidently 11 i A and i2 = ib. Apply Kirchoff's junction rule to the junction marked J in the figure in order to determine the remaining current iz.
(ii) Apply Kirchoff's voltage rule to the loop featuring the current source A, Rį and R3 in order to determine VA in terms of the known quantities.
(iii) Apply Kirchoff's voltage rule to the loop featuring the current source B, R2 and R3 in order to determine VB in terms of the known quantities.