Photo AI
Which value of resistance cannot be made by combining three 10 Ω resistors? A 3.3 Ω B 6.7 Ω C 15 Ω D 25 Ω - AQA - A-Level Physics - Question 30 - 2022 - Paper 1
Question 30
Which value of resistance cannot be made by combining three 10 Ω resistors? A 3.3 Ω B 6.7 Ω C 15 Ω D 25 Ω
Worked Solution & Example Answer:Which value of resistance cannot be made by combining three 10 Ω resistors? A 3.3 Ω B 6.7 Ω C 15 Ω D 25 Ω - AQA - A-Level Physics - Question 30 - 2022 - Paper 1
Step 1
Determine possible combinations of resistances
Answer
When combining resistors, the total resistance can either be calculated in series or parallel.
1. Series Combination:
When resistors are in series, the total resistance is the sum of the individual resistances:
totalResistance = R1 + R2 + R3 = 10 Ω + 10 Ω + 10 Ω = 30 Ω.
2. Parallel Combination:
In parallel, the formula is:
[ \frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} ]
For three identical resistors (R = 10 Ω):
[ \frac{1}{R_{total}} = \frac{1}{10} + \frac{1}{10} + \frac{1}{10} = \frac{3}{10} \Rightarrow R_{total} = \frac{10}{3} \approx 3.33 Ω ]
This shows that 3.3 Ω is possible. Therefore, we need to consider any possible configurations that yield 6.7 Ω, 15 Ω, or 25 Ω.
Step 2
Examine each option
Answer
A. 3.3 Ω
This can be achieved using parallel combination as shown above.
B. 6.7 Ω
Using two resistors in parallel and one in series gives:
[ R_{parallel} = \frac{10}{2} = 5 Ω ]
Adding the remaining resistor in series:
[ 5 Ω + 10 Ω = 15 Ω ]
So, this is not achievable.
C. 15 Ω
This can be achieved by combining two in parallel yielding 5 Ω, then adding a third in series (10 Ω):
[ R_{total} = 5 Ω + 10 Ω = 15 Ω ]
This is achievable.
D. 25 Ω
This can be achieved by combining two in series (20 Ω) and adding one in parallel, which yields greater than 20 Ω.
After analyzing these combinations, the resistance that cannot be made from three 10 Ω resistors is B. 6.7 Ω.