4.3 - Electricity: Electrical Circuits

Question 1

Kirchhoff’s First Law

Answer 1

The sum of the currents entering a junction (Node) in a circuit is equal to the sum of the currents leaving the junction.

Question 2

Mathematical Expression of Kirchoff’s 1st Law

Answer 2

I(1) + I(2) - 1(3) - I(4) - I(5) = 0

I(1) + I(2) = I(3) + I(4) + I(5) = 0

Question 3

Kirchhoff’s Second Law

Answer 3

In any closed loop, the sum of the e.m.f. is equal to the sum of the products of the current and the resistance.

Question 4

Mathematical Expresson of Kirchhoff’s 2nd Law

Answer 4

E(e.m.f.) = E (IR)

E = Sum of

Question 5

Current in Series Circuits

Answer 5

The current has the same value at any point in the circuit

Question 6

e.m.f. in Series Circuits

Answer 6

The e.m.f. of the cell is equal to the sum of the potential differences (V=IR) across the resistors

Question 7

The total resistance in Series Circuits

Answer 7

The total resistance of the circuit is equal to the sum of the individual resistors

R(t) = R(1) + R(2) + R(3) + …R(n)

Question 8

Prove that “R(t) = R(1) + R(2) + R(3)” is derived from V = IR

Answer 8

V = IR
V = V(1) + V(2) + V(3)
IR(t) = IR(1) + IR(2) + IR(3)
Factorising I gives I(R(t)) = I(R(1) + R(2) + R(3))
Dividing by I gives R(t) = R(1) + R(2) + R(3)

Question 9

Where are AMMETERS connected and what is their resistance?

Answer 9

• Connected in series

- Designed to have close-to-zero resistance in order to measure as much Current as possible

Question 10

Where are VOLTMETERS connected and what is their resistance?

Answer 10

• Connected in parallel

- Designed to have close-to-infinite resistance in order to measure as much Voltage as possible (blocks the Current)