T5D: Ohm's Law and series/parallel circuits

T5D Ohm's Law and series/parallel circuits

Ohm’s Law; Series and parallel circuits

Ohm’s Law links voltage, current and resistance, and it is the most-used formula in basic electronics. This group also asks which quantity stays constant in series and parallel circuits.

Ohm’s Law

Three quantities are tied together:

E is voltage in volts
I is current in amperes
R is resistance in ohms

The law can be arranged three ways:

Voltage: E = I x R
Current: I = E / R
Resistance: R = E / I

More voltage pushes more current. More resistance lowers current. Pick the formula for the unknown, plug in the two known numbers, and check the answer is sensible.

Worked examples

Finding resistance (R = E / I):

90 V and 3 A: 90 / 3 = 30 ohms
12 V and 1.5 A: 12 / 1.5 = 8 ohms
12 V and 4 A: 12 / 4 = 3 ohms

Finding current (I = E / R):

120 V across 80 ohms: 120 / 80 = 1.5 A
200 V across 100 ohms: 200 / 100 = 2 A
240 V across 24 ohms: 240 / 24 = 10 A

Finding voltage (E = I x R):

0.5 A through 2 ohms: 0.5 x 2 = 1 V
1 A through 10 ohms: 1 x 10 = 10 V
2 A through 10 ohms: 2 x 10 = 20 V

A common error is dividing when you should multiply, or flipping the division. Wrong answers on the exam are often the inverted result, such as 0.125 ohms instead of 8 ohms.

Series and parallel circuits

In a series circuit, components are connected end to end, giving the current only one path. The current is the same through every component, while the voltage divides among them.

In a parallel circuit, components are connected across the same two points, giving the current several paths. The voltage is the same across every branch, while the current divides among them.

A resonant circuit is a different idea (an inductor and capacitor tuned to one frequency), and a branch is just one path within a parallel circuit. Neither term describes the rule for equal current or equal voltage.

Key facts to memorize

E = I x R
I = E / R
R = E / I
Series: same current through all components
Parallel: same voltage across all components
Voltage in volts, current in amperes, resistance in ohms

Memory hooks

Use the triangle: put E on top and I and R on the bottom. Cover the unknown to see the formula.
Series = one road, same traffic everywhere. Parallel = same two ends, same voltage.

Questions in this group (14): answers shown

T5D01

What formula is used to calculate current in a circuit?
- A. I = E x R
- B. I = E / R ✓ Correct answer
- C. I = E2 x R
- D. I = E2 / R
Ohm's Law gives current as voltage divided by resistance: I = E / R. Current rises as voltage rises and falls as resistance rises.
T5D02

What formula is used to calculate voltage in a circuit?
- A. E = I x R ✓ Correct answer
- B. E = I / R
- C. E = I2 x R
- D. E = I2 / R
Ohm's Law gives voltage as current times resistance: E = I x R. Dividing would give a different quantity.
T5D03

What formula is used to calculate resistance in a circuit?
- A. R = E x I
- B. R = E / I ✓ Correct answer
- C. R = E + I
- D. R = E - I
Resistance equals voltage divided by current: R = E / I. This is Ohm's Law rearranged.
T5D04

What is the resistance of a circuit in which a current of 3 amperes flows when connected to 90 volts?
- A. 3 ohms
- B. 30 ohms ✓ Correct answer
- C. 1/30 ohm
- D. 270 ohms
R = E / I = 90 V / 3 A = 30 ohms. Divide the voltage by the current.
T5D05

What is the resistance of a circuit for which the applied voltage is 12 volts and the current flow is 1.5 amperes?
- A. 18 ohms
- B. 0.125 ohms
- C. 8 ohms ✓ Correct answer
- D. 13.5 ohms
R = E / I = 12 V / 1.5 A = 8 ohms. The 0.125 value comes from inverting the division.
T5D06

What is the resistance of a circuit that draws 4 amperes from a 12-volt source?
- A. 3 ohms ✓ Correct answer
- B. 16 ohms
- C. 48 ohms
- D. 8 ohms
R = E / I = 12 V / 4 A = 3 ohms. Voltage divided by current gives resistance.
T5D07

What is the current in a circuit with an applied voltage of 120 volts and a resistance of 80 ohms?
- A. 9600 amperes
- B. 200 amperes
- C. 0.667 amperes
- D. 1.5 amperes ✓ Correct answer
I = E / R = 120 V / 80 ohms = 1.5 A. Dividing voltage by resistance gives current.
T5D08

What is the current through a 100-ohm resistor connected across 200 volts?
- A. 20,000 amperes
- B. 0.5 amperes
- C. 2 amperes ✓ Correct answer
- D. 100 amperes
I = E / R = 200 V / 100 ohms = 2 A. Divide the voltage by the resistance.
T5D09

What is the current through a 24-ohm resistor connected across 240 volts?
- A. 2400 amperes
- B. 0.1 amperes
- C. 10 amperes ✓ Correct answer
- D. 5760 amperes
I = E / R = 240 V / 24 ohms = 10 A. Be careful to divide rather than multiply.
T5D10

What is the voltage across a 2-ohm resistor if a current of 0.5 amperes flows through it?
- A. 1 volt ✓ Correct answer
- B. 0.25 volts
- C. 2.5 volts
- D. 1.5 volts
E = I x R = 0.5 A x 2 ohms = 1 V. Multiply the current by the resistance.
T5D11

What is the voltage across a 10-ohm resistor if a current of 1 ampere flows through it?
- A. 1 volt
- B. 10 volts ✓ Correct answer
- C. 11 volts
- D. 9 volts
E = I x R = 1 A x 10 ohms = 10 V. Multiplying by 1 leaves the resistance value unchanged.
T5D12

What is the voltage across a 10-ohm resistor if a current of 2 amperes flows through it?
- A. 8 volts
- B. 0.2 volts
- C. 12 volts
- D. 20 volts ✓ Correct answer
E = I x R = 2 A x 10 ohms = 20 V. Multiply current by resistance to get voltage.
T5D13

In which type of circuit is the current always the same through all components?
- A. Series ✓ Correct answer
- B. Parallel
- C. Resonant
- D. Branch
In a series circuit there is only one path, so the same current flows through every component. In a parallel circuit the current divides among the branches.
T5D14

In which type of circuit is the voltage always the same across all components?
- A. Series
- B. Parallel ✓ Correct answer
- C. Resonant
- D. Branch
In a parallel circuit every branch is connected across the same two points, so each has the same voltage. In a series circuit the voltage divides among components.