DC motor with transistor driver in Arduino - Time & Space Complexity

Time Complexity: DC motor with transistor driver

O(1)

Understanding Time Complexity

We want to understand how the time the program takes changes as we control a DC motor using a transistor driver in Arduino code.

Specifically, we ask: how does the program's running time grow when we change the input size or control steps?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

int motorPin = 9;

void setup() {
  pinMode(motorPin, OUTPUT);
}

void loop() {
  analogWrite(motorPin, 255); // turn motor on full speed
  delay(1000);                // run for 1 second
  analogWrite(motorPin, 0);   // turn motor off
  delay(1000);                // wait for 1 second
}
    

This code turns a DC motor on and off repeatedly using a transistor driver connected to pin 9.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: The loop() function runs repeatedly forever.
• How many times: It repeats endlessly, turning the motor on and off each cycle.

How Execution Grows With Input

Here, the program runs the same steps over and over, regardless of input size.

Input Size (n)	Approx. Operations
10	Same fixed steps repeated 10 times
100	Same fixed steps repeated 100 times
1000	Same fixed steps repeated 1000 times

Pattern observation: The time per cycle stays the same; total time grows linearly with how many cycles run.

Final Time Complexity

Time Complexity: O(1)

This means each cycle of turning the motor on and off takes a fixed amount of time, no matter what.

Common Mistake

[X] Wrong: "The time to run the motor depends on the input size or speed value."

[OK] Correct: The code runs fixed delay times and fixed commands each cycle, so time per cycle does not change with input size.

Interview Connect

Understanding how loops and delays affect program timing helps you explain how embedded systems control hardware efficiently.

Self-Check

"What if we replaced the fixed delay with a loop that runs n times? How would the time complexity change?"

Practice

1. What is the main role of a transistor when controlling a DC motor with an Arduino?

easy

A. To act as a switch that controls the motor safely

B. To increase the motor speed directly

C. To power the Arduino board

D. To measure the motor's temperature

Solution

1. Step 1: Understand transistor function

   A transistor acts like a switch or amplifier in circuits.

2. Step 2: Apply to motor control

   In Arduino motor control, the transistor switches the motor on/off safely without damaging the board.

3. Final Answer:

   To act as a switch that controls the motor safely -> Option A

4. Quick Check:

   Transistor = switch for motor control [OK]

Hint: Think of transistor as a safe on/off switch for the motor [OK]

Common Mistakes:

• Confusing transistor with motor speed controller
• Thinking transistor powers the Arduino
• Assuming transistor measures anything

2. Which Arduino code snippet correctly sets a transistor pin to control a DC motor?

easy

A. pinMode(9, INPUT); digitalRead(9);

B. pinMode(9, INPUT); digitalWrite(9, HIGH);

C. pinMode(9, OUTPUT); digitalRead(9);

D. pinMode(9, OUTPUT); digitalWrite(9, HIGH);

Solution

1. Step 1: Set pin as output for controlling transistor

   To control a transistor, the Arduino pin must be OUTPUT.

2. Step 2: Write HIGH to turn motor on

   digitalWrite(9, HIGH) sends voltage to transistor base to switch motor on.

3. Final Answer:

   pinMode(9, OUTPUT); digitalWrite(9, HIGH); -> Option D

4. Quick Check:

   Output pin + HIGH = motor ON [OK]

Hint: Use OUTPUT mode and digitalWrite to control transistor [OK]

Common Mistakes:

• Setting pin as INPUT when controlling transistor
• Using digitalRead instead of digitalWrite
• Not setting pinMode before writing

3. What will be the effect of this Arduino code controlling a transistor connected to a DC motor?

int motorPin = 9;
void setup() {
  pinMode(motorPin, OUTPUT);
}
void loop() {
  analogWrite(motorPin, 128);
  delay(2000);
  analogWrite(motorPin, 0);
  delay(2000);
}

medium

A. Motor runs at half speed for 2 seconds, then stops for 2 seconds repeatedly

B. Motor runs at full speed continuously

C. Motor never runs because analogWrite is wrong

D. Motor runs at full speed for 2 seconds, then stops for 2 seconds repeatedly

Solution

1. Step 1: Understand analogWrite value

   analogWrite with 128 sets PWM to about 50% duty cycle, so motor runs at half speed.

2. Step 2: Analyze timing in loop

   Motor runs at half speed for 2 seconds, then analogWrite(0) stops motor for 2 seconds, repeating.

3. Final Answer:

   Motor runs at half speed for 2 seconds, then stops for 2 seconds repeatedly -> Option A

4. Quick Check:

   analogWrite(128) = half speed [OK]

Hint: PWM 128 means half speed, 0 means stop [OK]

Common Mistakes:

• Thinking analogWrite(128) is full speed
• Confusing analogWrite with digitalWrite
• Ignoring delay timing effects

4. Identify the error in this Arduino code controlling a transistor for a DC motor:

int motorPin = 9;
void setup() {
  pinMode(motorPin, INPUT);
}
void loop() {
  digitalWrite(motorPin, HIGH);
}

medium

A. Pin number 9 cannot be used for motor control

B. Pin is set as INPUT but digitalWrite is used

C. digitalWrite should be digitalRead

D. Missing delay in loop

Solution

1. Step 1: Check pinMode for transistor control

   Pin controlling transistor must be OUTPUT, not INPUT.

2. Step 2: Identify conflict with digitalWrite

   digitalWrite on an INPUT pin causes undefined behavior or no effect.

3. Final Answer:

   Pin is set as INPUT but digitalWrite is used -> Option B

4. Quick Check:

   OUTPUT needed for digitalWrite [OK]

Hint: Set pinMode to OUTPUT before digitalWrite [OK]

Common Mistakes:

• Using INPUT mode with digitalWrite
• Confusing digitalWrite with digitalRead
• Ignoring pinMode setup

5. You want to control a DC motor speed using PWM on pin 9 with a transistor driver. Which additional component is essential to protect your circuit from voltage spikes caused by the motor?

hard

A. An LED connected in parallel with the transistor

B. A capacitor connected to the Arduino 5V pin

C. A diode connected across the motor terminals

D. A resistor in series with the motor

Solution

1. Step 1: Understand motor voltage spikes

   When motor stops suddenly, it can create voltage spikes that damage components.

2. Step 2: Identify protection method

   A diode placed across motor terminals (flyback diode) safely redirects spikes, protecting transistor and Arduino.

3. Final Answer:

   A diode connected across the motor terminals -> Option C

4. Quick Check:

   Flyback diode protects circuit from spikes [OK]

Hint: Always add diode across motor for spike protection [OK]

Common Mistakes:

• Skipping diode and risking transistor damage
• Using resistor instead of diode for spike protection
• Confusing capacitor or LED as spike protection