1. PSC 4011 Electricity: What’s the connection?

2. PSC 4011: Series, Parallel & Combined circuits Series circuit: _One path for electric current. _All elements are connected simultaneously to the power source. _ If one element fails, electric conduction stops.

3. PSC 4011: Series, Parallel & Combined circuits Parallel circuit: _More than one path for electric current. _Each element is connected to the power source on its own. _ If one element fails, electric conduction continues in the others.

4. PSC 4011: Series, Parallel & Combined circuits Series circuits (Fig. 3.28, p. 3.49) ε = V 1 + V 2 + V 3 + … I t = I 1 = I 2 = I 3 = … R t = R 1 + R 2 + R 3 + … * R t is bigger than each individual resistance

5. PSC 4011: Series, Parallel & Combined circuits Series circuits (Fig. 3.28, p. 3.49) If you have several cells combined in series into a battery, the emf (V t ) will increase as a result of the addition of each cell’s emf.

6. PSC 4011: Series, Parallel & Combined circuits Practice: Calculate the equivalent resistance (total resistance) of a circuit, knowing that I = 3A and V 1 = V 3 = 6V, V 2 = 3V. What type of circuit is it? _ It is a series circuit since there is only one value for I _ R t = R 1 + R 2 + R 3 R t = (V 1 / I) + (V 2 / I) + (V 3 / I) R t = (6V / 3A) + (3V / 3A) + (6V / 3A) R t = 5 Ω

7. PSC 4011: Series, Parallel & Combined circuits Parallel circuits (Fig. 3.28, p. 3.49) ε = V 1 = V 2 = V 3 = … I t = I 1 + I 2 + I 3 + … 1/R t = 1/R 1 + 1/R 2 + 1/R 3 + … *R t is smaller than each individual resistance *I t is intensity near the power supply

8. PSC 4011: Series, Parallel & Combined circuits Series circuits (Fig. 3.28, p. 3.49) If you have several cells combined in parallel into a battery, the emf (V t ) will not change, but the discharge time will increase, since there will be less individual energy generation.

9. PSC 4011: Series, Parallel & Combined circuits Practice: Calculate the equivalent resistance (total resistance) of a circuit, knowing that V = 6V and I 1 = I 3 = 3A, I 2 = 6A. What type of circuit is it? _ It is a parallel circuit since there is more than one value for I _ 1/R t = 1/R 1 + 1/R 2 + 1/R 3 1/R t = (1 / V 1 / I) + (1 / V 2 / I) + (1 / V 3 / I) 1/R t = (I /V 1 ) + (I / V 2 ) + (I / V 3 ) 1/R t = (3A / 6V) + (6A / 6V) + (3A / 6V) 1/R t = 1/2 Ω + 1 Ω + 1/2 Ω 1/R t = 2 Ω- R t = 1/2 Ω or 0.5 Ω

10. PSC 4011: Series, Parallel & Combined circuits Combined circuits: Circuits that comprise elements connected in series and elements connected in parallel Calculations of V, I and R are done according to the type of circuit (series or parallel) the elements seem to be connected

11. PSC 4011: Series, Parallel & Combined circuits Practice Without calculations, find the value of I 4 and V 2 if we know that: I 1 = 1 AV 1 = 2 V I 2 = 5 AV 2 = ? I 3 = 3 AV 3 = 5 V I 4 = ?V 4 = 3 V I 4 = 1 A (series with I 1 ) V 2 = 5 V (parallel with V 3 )

12. PSC 4011: Series, Parallel & Combined circuits Practice: Calculate the equivalent resistance (total resistance) of the combined circuit in the picture. R t = R 1 + (1/R p = 1/R 2 + 1/R 3 ) + R 4 R t = 5 Ω + (1/R p = 1/8 Ω + 1/8 Ω ) + 6 Ω R t = 5 Ω + (1/R p = 2/8 Ω) + 6 Ω R t = 5 Ω + (R p = 4 Ω) + 6 Ω R t = 15 Ω

13. PSC 4011: Series, Parallel & Combined circuits Practice: Now that you know R t, calculate I t, and also calculate I 2 and I 3 I t = V t / R t I t = ε / R t I t = 60 V / 15 Ω I t = 4 A (I t = I 1 = I 4 series circuit) I t = I 2 + I 3 (parallel circuit) I 2 = I 3 (since R 2 = R 3 & V 2 = V 3 ) I 2 = I 3 = 2 A

14. PSC 4011: Series, Parallel & Combined circuits Practice: Now that you know R t, and each I, calculate V 1, V 2, V 3 and V 4. V 1 = (I t R 1 ) = (4A * 5Ω) = 20 V V 2 = (I 2 R 2 ) = (2A * 8Ω) = 16 V V 3 = (I 3 R 3 ) = (2A * 8Ω) = 16 V V 4 = (I t R 4 ) = (4A * 6Ω) = 24 V