Resistors & Cells Connected In Series & Parallel

CONTENT

• Resistors in series and parallel
• Cells in series and parallels
• Resistors in series: These are end to end connection.

CHARACTERISTICS

• Same current flow through each resistor I_T= I₁ = I₂ =I₃
• Potential difference across each resistor is different  V₁ ≠ V₂ ≠V₃
• P.d are additive V_T= V₁ + V₂ +V₃
• Power are additive
• Applied voltage equals the sum of different p.d  V_T= V₁ + V₂ +V₃
• Resistance are additive.

R_T = R₁ + R₂ + R₃ _______ for 3 resistors

R_T = R₁ + R₂ + R₃….. + Rn ___ for n numbers or resistors

RESISTORS IN PARALLEL

These are side by side connection.

CHARACTERISTICS

• Different resistors have their individual current
• P.d across each resistor is the same V_T= V₁ = V₂ = V₃
• Branch current are additive I_T = I₁ + I₂ +I₃
• Conductance are additive
• Power are additive

1/R_T = 1/R₁ + 1/R₂ + 1/R₃ ____ for 3 resistors

1/R_T = 1/R₁ + 1/R₂ + 1/R₃…..+ 1/Rn ____ for n numbers of resistors

EVALUATION

1. Differentiate between resistors connected in series and parallel
2. State the relationship between resistance and conductance

Cells in series: end to end connections

E_T = E + E + E = 3E

For n cells; E_T = n E

E_T = E₁ + E₂ + E₃

Cells in parallel: side by side connections

E_T = E+E+E/3 = 3E/3 = E

Calculations

If 2Ω, 3Ω, and 5Ω resistors are connected in (a) series (b) parallel, calculate the

equivalent resistance

(a)  R_T = 2+3+5 = 10Ω

(b)  1/R_T = 1/2 +1/3+1/5 = 15+10+6/30 = 31/30

R_T = 30/31Ω

EVALUATION

1. If 2Ω, 2Ω, and 1Ω resistors are connected in (a) series (b) parallel, calculate the equivalent resistance
2. Calculate the potential difference across a resistor of resistance 2KΩ that allows a current of 1mA to pass through it

READING ASSIGNMENT

Read more on series & parallel connections of resistors & cells – New school physics (pg 79)

GENERAL EVALUATION

1. State four types of motion and give an example each
2. What is the cause of motion.?

WEEKEND ASSIGNMENT

1. If four identical cells each 2volts are connected in series, the equivalent pd is ……… (a) 2v (b) 4v (c) 6v (d) 8v
2. If four identical cells each 2volts are connected in parallel, the equivalent pd is ……… (a) 2v (b) 4v (c) 6v (d) 8v
3. If 2Ω, 2Ω, and 1Ω resistors are connected in series the equivalent resistance (a) 5 Ω

(b) ½ Ω (c) 4 Ω (d) 2 Ω

4. If 2Ω, 2Ω, and 1Ω resistors are connected in parallel the equivalent resistance (a) 5 Ω (b) ½ Ω (c) 4 Ω (d) 2 Ω
5. Two resistors of resistance 1 Ω are connected in parallel to a 2 Ω resistor, the equivalent resistance is …….. (a) 4 Ω (b) 3 Ω (c) 2 Ω (d) 1 Ω

THEORY

1. A battery of 15v and internal resistance 5Ω is connected to a resistor 0f 20Ω. Calculate the value of (a) electric current (b) terminal voltage   (c) lost voltage.
2. If 8c of charge passes through a wire at a steady rate in 2s. Calculate the Current.