Supplement to Circuits Analysis Zhou Lingling SJTU Zhou Lingling

Outline Basic Concepts Basic laws Useful theorems SJTU Zhou Lingling

Basic Concepts Current, voltage and power Sources Ohm’s law Independent sources Controlled sources Ohm’s law Kirchhoff’s current and voltage laws Passive elements Resistor R Capacitor C Inductor L SJTU Zhou Lingling

Current Direction and value Constant value and instantaneous value SJTU Zhou Lingling

Current Two different methods of labeling the same current. SJTU Zhou Lingling

Current (a,b) Inadequate definitions of a current. (c) the correct definition of i1(t). SJTU Zhou Lingling

Voltage Voltage across a terminal pair is a measure of the work required to move charge through the element. Voltage can exist between a pair of terminals whether a current is flowing or not. Distinguish between energy supplied to or by the element. SJTU Zhou Lingling

Voltage (a, b) These are inadequate definitions of a voltage. (c) A correct definition includes both a symbol for the variable and a plus-minus symbol pair. SJTU Zhou Lingling

Voltage (a,b) Terminal B is 5 V positive with respect to terminal A; (c,d) terminal A is 5 V positive with respect to terminal B. SJTU Zhou Lingling

Power SJTU Zhou Lingling

Power If the current arrow is directed into the “ +” marked terminal of an element, then p = vi yields the absorbed power. A negative value indicates that power is actually being generated by the element. If the current arrow is directed out of the “ +” terminal of an element, then p = vi yields the supplied power. A negative value in this case indicates that power is actually being absorbed instead of generated. SJTU Zhou Lingling

Power Find the power absorbed by each element in the circuit below. SJTU Zhou Lingling

Sources Independent sources Controlled sources Voltage source Current source Controlled sources Voltage-controlled current source (VCCS) Voltage-controlled voltage source (VCVS) Current-controlled current source (CCCS) Current-controlled voltage source (CCVS) SJTU Zhou Lingling

Independent Voltage Source Symbol for: (a) DC voltage source (b) Battery (c) ac voltage source An independent voltage source is characterized by a terminal voltage which is completely independent of the current through it. SJTU Zhou Lingling

independent Current Source Symbol for an independent current source. Current source can deliver infinite power from its terminals, because it produces the same finite current for any voltage across it, no matter how large the voltage may be. SJTU Zhou Lingling

Controlled Sources (a) current-controlled current source; (b) voltage-controlled current source; (c) voltage-controlled voltage source; (d) current-controlled voltage source. SJTU Zhou Lingling

Controlled Sources In the circuit below ,if v2 is known to be 3 V, find vL . SJTU Zhou Lingling

Ohm’s law v = i R or i = SJTU Zhou Lingling

Ohm’s law Conductance Absorbed power SJTU Zhou Lingling

Nodes, Paths, Loops, and Branches A point at which two or more elements have a common connection is called a node. If no node is encountered more than once, then the set of nodes and elements that we have passed through is defined as a path. If the node at which we started is the same as the node on which we ended, then the path is, by definition, a closed path or loop. We define a branch as a single path in a network, composed of one simple element and node at each end of the element. SJTU Zhou Lingling

Nodes, Paths, Loops, and Branches A circuit containing three nodes and five branches. (b) Node 1 is redrawn to look like two nodes; it is still one node. SJTU Zhou Lingling

Kirchhoff’s Current Law The algebraic sum of the currents entering any node is zero. SJTU Zhou Lingling

Kirchhoff’s Current Law Figure 3.2 SJTU Zhou Lingling

Kirchhoff’s Voltage Law The algebraic sum of the voltages around any closed path is zero. SJTU Zhou Lingling

The Single Loop Circuit Simple resistive circuit. All the element in a circuit that carry the same current are said to be connected in series. SJTU Zhou Lingling

The Single Loop Circuit Simple resistive circuit. All the element in a circuit that carry the same current are said to be connected in series. SJTU Zhou Lingling

The Single Node-pair Circuit Simple resistive circuit. Elements in a circuit hacing a common voltage across them are said to be connected in parallel. SJTU Zhou Lingling

Resistor Series combination of N resistors. (b) Electrically equivalent circuit. SJTU Zhou Lingling

Resistor SJTU Zhou Lingling

Resistor A circuit with N resistors in parallel. Equivalent circuit. SJTU Zhou Lingling

Resistor Beginning with a simple KCL equation, or Thus, A special case worth remembering is SJTU Zhou Lingling

Electrical symbol and current-voltage conventions for a capacitor. SJTU Zhou Lingling

Capacitor (c) (d) N capacitors connected in series; (b) equivalent circuit; (c) N capacitors connected in parallel; (d) equivalent circuit to (c). SJTU Zhou Lingling

Inductor Electrical symbol and current-voltage conventions for an inductor. SJTU Zhou Lingling

Inductor N inductors connected in series; Equivalent circuit; SJTU Zhou Lingling

Inductor (c) N inductors connected in parallel; (d) equivalent circuit for circuit in (c). SJTU Zhou Lingling

Voltage Division We may find v2 by applying KVL and Ohm’s law: so Thus, An illustration of voltage division. or For a string of N series resistors, we may write: SJTU Zhou Lingling

Voltage Division Use voltage division to determine vx in the adjacent circuit. SJTU Zhou Lingling

Current Division The current flowing through R2 is or For a parallel combination of N resistors, the current through Rk is An illustration of current division. SJTU Zhou Lingling

Current Division Determine the current Ix if I1 = 100 mA. SJTU Zhou Lingling

Thévenin’s Theorem. SJTU Zhou Lingling

Norton’s Theorem. SJTU Zhou Lingling

Thévenin’s Theorem Application Determine the Thévenin and Norton Equivalents of Network A in (a). SJTU Zhou Lingling

Thévenin’s Theorem Application Thévenin’s theorem applied to simplify the circuit of (a) to that in (b). SJTU Zhou Lingling

The Source-Absorption Theorem. SJTU Zhou Lingling

The Source-Absorption Theorem. SJTU Zhou Lingling