Electric Circuits PDF

Samer Issa Samer Issa 1 Samer Issa 2   Materials in general have a characteristic behavior of resisting the flow of electric charge. This physical property, or ability to resist current, is known as resistance and is represented by the symbol R.  The resistance o...

Samer Issa Samer Issa 1 Samer Issa 2   Materials in general have a characteristic behavior of resisting the flow of electric charge. This physical property, or ability to resist current, is known as resistance and is represented by the symbol R.  The resistance of any material with a uniform cross- sectional area A depends on A and its length l , as shown in Fig. 2.1 Where  is known as the resistivity of the material in ohm-meters Samer Issa 3  Ohm’s law states that the voltage v across a resistor R is directly proportional to the current i flowing through the resistor. The resistance R of an element denotes its ability to resist the flow of electric current; it is measured in ohms (Ω). Samer Issa 4  A short circuit is a circuit element with resistance approaching zero.  An open circuit is a circuit element with resistance approaching infinity. Samer Issa 5  The power dissipated by a resistor can be expressed in terms of R. We should note two things from Equation above 1.The power dissipated in a resistor is a nonlinear function of either current or voltage. 2. Since R is positive quantities, the power dissipated in a resistor is always positive. Thus, a resistor always absorbs power from the circuit. This confirms the idea that a resistor is a passive element, incapable of generating energy. Samer Issa 6  A branch represents a single element such as a voltage source or a resistor.  A node is the point of connection between two or more branches.  A loop is any closed path in a circuit.  Two or more elements are in series if they exclusively share a single node and consequently carry the same current.  Two or more elements are in parallel if they are connected to the same two nodes and consequently have the same voltage across them. Samer Issa 7 Determine the number of branches and nodes in the circuit shown in figure below. Identify which elements are in series and which are in parallel. Samer Issa 8 Determine the number of branches and nodes in the circuit of Figure below. Samer Issa 9 Kirchhoff ’s current law (KCL) states that the algebraic sum of the currents entering a node is equal to the sum of the currents leaving the node. Samer Issa 10 Samer Issa 11  Kirchhoff’s voltage law (KVL) states that the algebraic sum of all voltages around a closed path (or loop) is zero.  where M is the number of voltages in the loop (or the number of branches in the loop) and v m is the mth voltage. Samer Issa 12 Samer Issa 13  The two resistors are in series, since the same current i flows in both of them. Samer Issa 14  The equivalent resistance of any number of resistors connected in series is the sum of the individual resistances.  For N resistors in series then,  To determine the voltage across each resistor in Figure 2.29 by principle of voltage division Samer Issa 15  Where two resistors are connected in parallel and therefore have the same voltage across them. Samer Issa 16  Applying KCL at node a gives the total current i as  where Req is the equivalent resistance of the resistors in parallel:  The equivalent resistance of two parallel resistors is equal to the product of their resistances divided by their sum.  with N resistors in parallel. The equivalent resistance is Samer Issa 17  To obtain current i1 and i2 in Figure 2.31 by principle of current division  Suppose one of the resistors in Fig. 2.31 is zero, say R2= 0 ; that is R2, is a short circuit, as shown in Fig. 2.33(a). implies that i1 = 0 and i2= i. This means that the entire current i bypasses R1 and flows through the short circuit R2= 0, the path of least resistance. Samer Issa 18  Suppose R2= ∞ that is, R2is an open circuit, as shown in Fig. 2.33(b). The current still flows through the path of least resistance, R1 Samer Issa 19 For the circuit in Figure below. Find voltages v1 and v2. Samer Issa 20 Determine vo and i in the circuit shown in Figure. Samer Issa 21 Find current io and voltage vo in the circuit shown in Figure. Samer Issa 22 Find Req Samer Issa 23 Calculate the equivalent resistance Rab in the circuit in Figure shown Samer Issa 24 Find io and vo and in the circuit shown in Figure. Calculate the power dissipated in the 3Ω resistor. Samer Issa 25 For the circuit shown in Figure, find: (a) V1 and V2 (b) The power dissipated in all resistors. (c) The power supplied by the current source. Samer Issa 26 Samer Issa 27 Delta to Wye Conversion Wye to Delta Conversion Samer Issa 28 Samer Issa 29 Obtain the equivalent resistance Rab for the circuit shown in Figure and use it to find current i. Samer Issa 30