Ohm's Law and Electrical Calculations in the UK

Ohm's Law Basics

• Ohm's Law describes the relationship between voltage (V), current (I), and resistance (R) in an electrical circuit.
• The formula for Ohm's Law is V = IR, where V is voltage in volts, I is current in amperes, and R is resistance in ohms.
• The standard voltage in the UK is 230V.
• Power (P) in watts can be calculated using the formulas P = VI, P = I²R, or P = V²/R.

Practical Application in UK Context

• Using Ohm's Law, one can calculate the current drawn by an appliance if the voltage and resistance are known, or the resistance if voltage and current are known.
• In UK households, understanding Ohm's Law is crucial for calculating safe current levels for appliances and wiring.
• Overcurrent in circuits will cause wires to overheat potentially starting fires
• Circuit breakers and fuses are designed to prevent current over the limits of the wires
• Fuses ratings are chosen so they blow before the wires are overloaded

Calculations with 230V

• Given a 230V supply, the current through a 100-ohm resistor would be I = V/R = 230V/100 ohms = 2.3 amps.
• With a 230V supply, an appliance drawing 5 amps would have a resistance of R = V/I = 230V/5 amps = 46 ohms.
• The example questions below use a voltage of 230V as is the typical voltage of the UK electrical system.

Question 1

• A kettle with a resistance of 23 ohms is connected to a 230V UK mains supply. What current does it draw?
• (A) 0.1 A (B) 1 A (C) 10 A (D) 100 A
• Correct answer: (C) 10 A. Calculation: I = V/R = 230V / 23 ohms = 10A.

Question 2

• An electric heater draws a current of 5 amps from a 230V UK mains supply. What is its resistance?
• (A) 4.6 ohms (B) 46 ohms (C) 1150 ohms (D) 0.02 ohms
• Correct answer: (B) 46 ohms. Calculation: R = V/I = 230V / 5A = 46 ohms.

Question 3

• A light bulb has a resistance of 529 ohms and is connected to a 230V UK mains supply. What current flows through it?
• (A) 0.435 A (B) 2.3 A (C) 121,370 A (D) 43.5 A
• Correct answer: (A) 0.435 A. Calculation: I = V/R = 230V / 529 ohms = 0.435 A.

Question 4

• A device with a resistance of 11.5 ohms is connected to a 230V UK mains supply. What current does it draw?
• (A) 20 A (B) 0.05 A (C) 2645 A (D) 2 A
• Correct answer: (A) 20 A. Calculation: I = V/R = 230V / 11.5 ohms = 20A.

Question 5

• An appliance draws 8 amps from a 230V UK mains supply. What is its resistance?
• (A) 28.75 ohms (B) 1840 ohms (C) 0.035 ohms (D) 2.875 ohms
• Correct answer: (A) 28.75 ohms. Calculation: R = V/I = 230V / 8A = 28.75 ohms.

Question 6

• A heating element with a resistance of 50 ohms is connected to a 230V UK mains supply. What current does it draw?
• (A) 4.6 A (B) 11500 A (C) 0.217 A (D) 46 A
• Correct answer: (A) 4.6 A. Calculation: I = V/R = 230V / 50 ohms = 4.6 A.

Question 7

• If a toaster draws 4A from the 230V UK power supply what is the resistance of the toaster?
• (A) 57.5 Ohms (B) 920 Ohms (C) 0.017 Ohms (D) 40 Ohms
• Correct answer: (A) 57.5 Ohms. Calculation: R = V/I = 230V / 4A = 57.5 ohms.

Question 8

• What is the current flowing through a 20 Ohm resistor connected to the 230V UK mains?
• (A) 4.6 A (B) 11.5 A (C) 0.087 A (D) 4600 A
• Correct answer: (B) 11.5 A. Calculation: I = V/R = 230V / 20 ohms = 11.5 A.

Question 9

• In a parallel circuit with a 230V supply, a 100-ohm resistor and a 200-ohm resistor are connected. What is the total current drawn from the supply?
• (A) 3.45 A (B) 2.3 A (C) 1.15 A (D) 1.73 A
• Correct answer: (A) 3.45 A. Calculation: Current through 100-ohm resistor (I1) = 230V / 100 ohms = 2.3A, Current through 200-ohm resistor (I2) = 230V / 200 ohms = 1.15A. Total current (I) = I1 + I2 = 2.3A + 1.15A = 3.45A.

Question 10

• A phone charger with resistance 460 Ohms is connected to the 230V UK mains, what current flows?
• (A) 2 A (B) 0.5 A (C) 1 A (D) 1.5 A
• Correct answer: (B) 0.5 A. Calculation: I = V/R = 230V / 460 ohms = 0.5 A.