Battery capacity (kWh) and range relationship in EV Technology - Practice Problems & Coding Challenges

Challenge - 5 Problems

🧠 Conceptual

intermediate

Understanding the basic relationship between battery capacity and range

Which statement best describes how battery capacity in kilowatt-hours (kWh) affects the driving range of an electric vehicle (EV)?

A A higher battery capacity generally increases the driving range because it stores more energy.

B Battery capacity affects only the charging speed, not the driving range.

C A smaller battery capacity always results in a longer driving range.

D Battery capacity does not affect driving range; only the vehicle's weight matters.

💡 Hint

Think about how storing more energy in the battery might influence how far the car can travel.

Battery capacity measured in kWh indicates how much energy the battery can store. More stored energy means the vehicle can run longer before needing a recharge, thus increasing the driving range.

📋 Factual

intermediate

Calculating range from battery capacity and efficiency

If an electric vehicle has a battery capacity of 60 kWh and consumes 15 kWh per 100 kilometers, what is its approximate driving range?

A 400 kilometers

B 900 kilometers

C 250 kilometers

D 100 kilometers

💡 Hint

Divide the total battery capacity by the energy consumption per 100 km, then multiply by 100.

Range = (Battery capacity / Consumption per 100 km) × 100 = (60 kWh / 15 kWh) × 100 = 4 × 100 = 400 km.

🔍 Analysis

advanced

Impact of vehicle efficiency on range despite battery size

Two electric vehicles have the same battery capacity of 75 kWh. Vehicle A consumes 20 kWh per 100 km, and Vehicle B consumes 15 kWh per 100 km. Which vehicle has a longer range and why?

A Vehicle A has a longer range because it uses more energy per 100 km.

B Both vehicles have the same range because battery capacity is the same.

C Vehicle A has a longer range because it has a bigger battery.

D Vehicle B has a longer range because it is more energy efficient.

💡 Hint

Consider how energy consumption affects how far the stored energy can take the vehicle.

Even with the same battery size, the vehicle that uses less energy per distance (Vehicle B) can travel farther, so Vehicle B has the longer range.

❓ Comparison

advanced

Comparing range increase from battery capacity growth

If an electric vehicle's battery capacity increases from 50 kWh to 75 kWh, by what percentage does the driving range increase assuming energy consumption stays constant?

A 25% increase

B 50% increase

C 75% increase

D 100% increase

💡 Hint

Calculate the percentage increase from 50 to 75 kWh.

The increase is (75 - 50) / 50 × 100% = 25 / 50 × 100% = 50% increase in battery capacity and thus range.

❓ Reasoning

expert

Why increasing battery capacity alone may not double EV range

Why might doubling the battery capacity of an electric vehicle not result in exactly double the driving range?

A Because doubling battery capacity always doubles the range without exceptions.

B Because battery capacity has no effect on driving range.

C Because larger batteries add weight, which can reduce efficiency and increase energy consumption.

D Because electric vehicles do not use battery energy for driving.

💡 Hint

Think about how adding more battery cells might affect the vehicle's weight and energy use.

Larger batteries weigh more, which can make the vehicle less efficient and increase energy use per kilometer. This reduces the expected range gain from simply doubling battery capacity.

Practice

1. What does the battery capacity measured in kWh represent in an electric vehicle (EV)?

easy

A. The speed at which the EV can travel

B. The weight of the battery

C. The total amount of energy the battery can store

D. The time it takes to charge the battery fully

Solution

1. Step 1: Understand battery capacity meaning

   Battery capacity in kWh shows how much energy the battery can hold at full charge.

2. Step 2: Differentiate from other factors

   Speed, weight, and charging time are different characteristics, not battery capacity.

3. Final Answer:

   The total amount of energy the battery can store -> Option C

4. Quick Check:

   Battery capacity = energy stored [OK]

Hint: Battery capacity means stored energy, not speed or weight [OK]

Common Mistakes:

• Confusing capacity with charging time
• Thinking capacity means battery weight
• Mixing capacity with vehicle speed

2. Which formula correctly relates battery capacity (kWh), energy efficiency (kWh per mile), and driving range (miles)?

easy

A. Range = Battery capacity x Energy efficiency

B. Range = Battery capacity ÷ Energy efficiency

C. Range = Energy efficiency ÷ Battery capacity

D. Range = Battery capacity + Energy efficiency

Solution

1. Step 1: Understand units and relationship

   Energy efficiency is how many kWh are used per mile, so dividing capacity by efficiency gives miles.

2. Step 2: Apply correct formula

   Range (miles) = Battery capacity (kWh) ÷ Energy used per mile (kWh/mile).

3. Final Answer:

   Range = Battery capacity ÷ Energy efficiency -> Option B

4. Quick Check:

   Range = Capacity ÷ Efficiency [OK]

Hint: Divide capacity by efficiency to get range [OK]

Common Mistakes:

• Multiplying capacity by efficiency instead of dividing
• Adding capacity and efficiency
• Reversing the division order

3. An EV has a battery capacity of 75 kWh and an energy efficiency of 0.25 kWh per mile. What is its approximate driving range?

medium

A. 300 miles

B. 18.75 miles

C. 75 miles

D. 0.0033 miles

Solution

1. Step 1: Identify given values

   Battery capacity = 75 kWh, Energy efficiency = 0.25 kWh/mile.

2. Step 2: Calculate range using formula

   Range = 75 ÷ 0.25 = 300 miles.

3. Final Answer:

   300 miles -> Option A

4. Quick Check:

   75 ÷ 0.25 = 300 [OK]

Hint: Divide 75 by 0.25 to get 300 miles range [OK]

Common Mistakes:

• Multiplying instead of dividing
• Confusing units and calculating incorrectly
• Choosing the smallest number thinking it's correct

4. A student wrote this formula to calculate EV range: range = battery_capacity * energy_efficiency. What is wrong with this formula?

medium

A. It should multiply battery capacity by the square of energy efficiency

B. It should add battery capacity and energy efficiency

C. The formula is correct as is

D. It should divide battery capacity by energy efficiency, not multiply

Solution

1. Step 1: Recall correct formula for range

   Range equals battery capacity divided by energy used per mile, not multiplied.

2. Step 2: Identify error in student's formula

   Multiplying capacity by efficiency gives wrong units and wrong result.

3. Final Answer:

   It should divide battery capacity by energy efficiency, not multiply -> Option D

4. Quick Check:

   Range = Capacity ÷ Efficiency, not x [OK]

Hint: Range = capacity ÷ efficiency, not multiply [OK]

Common Mistakes:

• Using multiplication instead of division
• Assuming formula is correct without checking units
• Adding values instead of dividing

5. You want an EV that can travel at least 250 miles on a single charge. If the car's energy efficiency is 0.3 kWh per mile, what minimum battery capacity (in kWh) should you look for?

hard

A. 75 kWh

B. 83.33 kWh

C. 250 kWh

D. 0.0012 kWh

Solution

1. Step 1: Understand the requirement and formula

   Range = Battery capacity ÷ Energy efficiency. Rearranged: Battery capacity = Range x Energy efficiency.

2. Step 2: Calculate minimum battery capacity

   Battery capacity = 250 miles x 0.3 kWh/mile = 75 kWh. But check options carefully.

3. Step 3: Recalculate carefully

   250 x 0.3 = 75 kWh, but 83.33 kWh is 83.33 kWh, 75 kWh is 75 kWh. The correct minimum is 75 kWh.

4. Final Answer:

   75 kWh -> Option A

5. Quick Check:

   Capacity = Range x Efficiency = 75 kWh [OK]

Hint: Multiply range by efficiency to find capacity [OK]

Common Mistakes:

• Dividing instead of multiplying
• Choosing wrong option due to calculation error
• Confusing range and capacity units