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EEE (2110005) - ACTIVE LEARNING ASSIGNMENT Presented by: Divyang Vadhvana(130120116086) Branch: Information Technology Electrical circuits often contain one or more resistors grouped together and attached to an energy source, such as a battery. The following symbols are often used: Ground + - + - + - + - Battery + - Resistor Resistors are said to be connected in series when there is a single path for the current. I R1 VT R2 R3 Only one current For series connections: The current I is the same for each resistor R1, R2 and R3. The energy gained through E is lost through R1, R2 and R3. The same is true for voltages: I = I1 = I2 = I3 VT = V1 + V2 + V3 The equivalent resistance Re of a number of resistors connected in series is equal to the sum of the individual resistances. VT = V1 + V2 + V3 ; (V = IR) I R1 VT R2 R3 Equivalent Resistance ITRe = I1R1+ I2R2 + I3R3 But . . . IT = I1 = I2 = I3 Re = R1 + R2 + R3 The output direction from a source of emf is from + side: - a + b E Thus, from a to b the potential increases by E; From b to a, the potential decreases by E. A R AB: V = +9 V – 3 V = +6 V 3V BA: V = +3 V - 9 V = -6 V B - 9V + + Example: Find V for path AB and then for path BA. Consider the simple series circuit drawn below: D A - 2 C - 15 V + + 4 3V B Path ABCD: Energy and V increase through the 15-V source and decrease through the 3-V source. E = 1 5 V -3 V = 1 2 V The net gain in potential is lost through the two resistors: these voltage drops are IR2 and IR4, so that the sum is zero for the entire loop. R2 Resistance Rule: Re = R C u r r e n t: Voltage Rule: E I R E = IR R1 E2 E1 A complex circuit is one containing more than a single loop and different current paths. At junctions m and n: I1 = I2 + I3 or I2 + I3 = I1 Junction Rule: I (enter) = I (leaving) I3 R3 R1 m E2 n I1 R2 E1 I2 Resistors are said to be connected in parallel when there is more than one path for current. Parallel Connection: 2 4 6 Series Connection: 2 4 6 For Parallel Resistors: V2 = V4 = V6 = VT I2 + I 4 + I 6 = I T For Series Resistors: I2 = I 4 = I 6 = I T V2 + V4 + V6 = VT VT = V 1 = V 2 = V 3 IT = I1 + I2 + I3 VT Parallel Connection: R1 V Ohm’s law: I R V V T 1 V 2 V 3 R R e 1 R 2 R 3 R2 R3 1 1 1 1 R R e 1 R 2 R 3 The equivalent resistance for Parallel resistors: 1 N 1 Re i1 Ri The equivalent resistance Re for two parallel resistors is the product divided by the sum. 1 1 1 ; R R R e 1 2 Example: VT R1 6 R2 3 RR Re 1 2 R1 R2 (3 )(6 ) R e 3 6 Re = 2 In complex circuits resistors are often connected in both series and parallel. R 1 In such cases, it’s best to use rules for series and parallel resistances to reduce the circuit to a simple circuit containing one source of emf and one equivalent resistance. VT R2 VT R3 Re Kirchoff’s first law: The sum of the currents entering a junction is equal to the sum of the currents leaving that junction. Junction Rule: I (enter) = I (leaving) Kirchoff’s second law: The sum of the emf’s around any closed loop must equal the sum of the IR drops around that same loop. Voltage Rule: E = IR When applying Kirchoff’s laws you must assume a consistent, positive tracing direction. When applying the voltage rule, emf’s are positive if normal output direction of the emf is with the assumed tracing direction. If tracing from A to B, this emf is considered positive. If tracing from B to A, this emf is considered negative. A E + A E + B B When applying the voltage rule, IR drops are positive if the assumed current direction is with the assumed tracing direction. If tracing from A to B, this IR drop is positive. If tracing from B to A, this IR drop is negative. A I + A I + B B 1. Assume possible consistent flow of currents. 2. Indicate positive output R1 directions for emf’s. 3. Indicate consistent tracing direction. (clockwise) Junction Rule: I2 = I1 + I3 Voltage Rule: E = IR E1 + E2 = I1R1 + I2R2 + I1 Loop I E2 R3 E1 R2 I2 I3 E3 4. Voltage rule for Loop II: Assume counterclockwise positive tracing direction. Voltage Rule: E = IR Bottom Loop (II) R1 Yes! - E2 - E3 = -I2R2 - I3R3 Loop I R3 E1 R2 E2 E2 + E3 = I2R2 + I3R3 Would the same equation apply if traced clockwise? I1 I2 I3 Loop II + E3 5. Voltage rule for Loop III: Assume counterclockwise positive tracing direction. + Voltage Rule: E = IR Outer Loop (III) R1 Yes! E3 - E1 = I1R1 - I3R3 Loop I R3 E1 R2 E2 E3 – E1 = -I1R1 + I3R3 Would the same equation apply if traced clockwise? I1 I2 I3 Loop II + E3 6. Thus, we now have four independent equations from Kirchoff’s laws: + I2 = I 1 + I 3 Outer Loop (III) R1 I1 Loop I R2 E2 E1 + E2 = I1R1 + I2R2 E2 + E3 = I2R2 + I3R3 E3 - E1 = -I1R1 + I3R3 R3 E1 I2 I3 Loop II + E3 Rules for a simple, single loop circuit containing a source of emf and resistors. Resistance Rule: Re = R C u r r e n t: E I R E = IR Single Loop - 2 3 3V C - A 18 V + + Voltage Rule: D B For resistors connected in series: For series connections: I = I1 = I2 = I3 VT = V1 + V2 + V3 Re = R1 + R2 + R3 Re = R 2 3 1 12 V Resistors connected in parallel: V = V1 = V2 = V3 IT = I1 + I2 + I3 For parallel connections: 1 N 1 Re i1 Ri RR Re 1 2 R1 R2 Parallel Connection R1 R2 R3 VT 2 12 V 4 6 Kirchoff’s first law: The sum of the currents entering a junction is equal to the sum of the currents leaving that junction. Junction Rule: I (enter) = I (leaving) Kirchoff’s second law: The sum of the emf’s around any closed loop must equal the sum of the IR drops around that same loop. Voltage Rule: E = IR