3. D.C. Circuits

Question 1

Summary of Series Circuit

Effective Resistance, Current, p.d. across Each Resistor

Answer 1

Series circuit:

• Effective resistance (R_e): R_e = R₁ + R₂ + … + R_n
• Current in the circuit (I_o): I_o = I₁ = I₂ = I₃
• p.d. across any 1 resistor: ϵ = V₁ + V₂ + … + V_n

V_n ∝ R_n (p.d. across resistor is proportional to its resistance)
V₁ : V₂ : ϵ = R₁ : R₂ : (R₁ + R₂)

Voltage Divider Formula:
V_n/ϵ = R_n/R_e

Question 2

Summary of Parallel Circuit

Effective Resistance, Current, p.d. across Each Branch

Answer 2

Parallel circuit:

• Effective resistance (R_e): R_e = (1/R₁ + 1/R₂ + … + 1/R_n)^-1
• Current in the circuit (I_o): I_o = I₁ + I₂ + … + I_n
• p.d. across any 1 branch: V_o = V₁ = V₂ = … = V_n

I_n ∝ 1/R_n (current flowing in each branch is inversely proportional to the resistance of that branch)

Current Divider Formula:
I_n/I_o = R_e/R_n

Question 3

Bypass vs Short Circuit

Answer 3

Bypass:

• Alternative path of 0 resistance for current to flow

Short circuit:

• Bypass of every component which results in a very large current which can generate enough heat to start a fire

Question 4

Light Dependant Resistor (LDR)

Answer 4

Light dependant resistor is a resistor which resistance varies with the intensity of light falling on it:

• As brightness of the surroundings decreases, resistance of LDR increases
• As brightness of the surroundings increases, resistance of LDR decreases

resistance ∝ 1/brightness

Question 5

Thermistor

Answer 5

Thermistor is a resistor which resistance varies with temperature:

• As temperature of the surroundings decreases, resistance of thermistor increases
• As temperature of the surroundings increases, resistance of the thermistor decreases

resistance ∝ 1/temperature

This is for negative temperature coefficient (NTC) thermistor. Some thermistors behave in reverse.