Electric Circuit Series and Parallel Arrangement of Cells and Resistors

Electric circuit Presentation Click on the slides:

(a) Cell Arrangement:

(i) Cells in Series:

The total emf is the sum of all the emfs.

(ii) Cells in Parallel:

All emfs are equal.

E_T = E1 or E2 or E3, if E1 = E2 = E3, i.e, all emfs are equal.

E_T = E3, (emf with the highest value), if E3 > E2 > E1

(b) Resistors Arrangement:

(i) Resistors in Series:

V_T = V₁ + V₂ + V₃       

(Circuital components in series have the same I but different V)

But V = IR

∴ IRT = IR1 + IR2 + IR3

IRT = I(R1 + R2 + R3)

Dividing through by I, we have R_T = (R₁ + R₂ +R₃)

(ii) Resistors in Parallel:

IT=I1+I2+I3

But I=VR

∴VRT=VR1+VR2+VR3∴V(1RT)=V(1R1+1R2+1R3)

Dividing through by V, we have:

(1RT)=(1R1+1R2+1R3)=R1R2+R1R3+R2R3R1R2R3

Examples:

1. If four 3 resistors are connected a) in series b) in parallel, find their net resistance in each case.

Solution:

(a) In series,

RT=R1+R2+R3+R4=3+3+3+3=12Ω

(b) In parallel,

2. Three cells of value 2V, 2V and 3V are connected (a) in series (b) in parallel. Find their total emf in  each case.

Solution:

(a) In series,

ET=E1+E2+E3=2+2+3=7V

(b) In parallel, since 3V has the highest emf among the three cells, E_T = 3V

EVALUATION (POST YOUR ANSWERS USING THE QUESTION BOX BELOW FOR EVALUATION AND DISCUSSION):

1. State the formula for finding the net emf and resistance when these components are in a) series b) parallel.
2. When two cells of value 2V and 3V are in parallel, what is their total emf?