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Two resistances R1 and R2 give combined resistance of 4.5 ohms when in series and 1 ohm when in parallel. The resistance are
- a)3 ohms and 6 ohms
- b)3 ohms and 9 ohms
- c)1.5 ohms and 3 ohms
- d)1.5 ohms and 0.5 ohms
Correct answer is option 'C'. Can you explain this answer?
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Two resistances R1 and R2 give combined resistance of 4.5 ohms when in...
Given:
Resistance in series: R_series = 4.5 ohms
Resistance in parallel: R_parallel = 1 ohm
To find:
The resistance values of R1 and R2.
Solution:
Let's start by calculating the resistance in series. When two resistances are connected in series, their resistances add up.
Resistance in series:
R_series = R1 + R2
Substituting the given value, we get:
4.5 ohms = R1 + R2 ...........(1)
Next, let's calculate the resistance in parallel. When two resistances are connected in parallel, their reciprocal values add up, and the sum is the reciprocal of the total resistance.
Resistance in parallel:
1/R_parallel = 1/R1 + 1/R2
Substituting the given value, we get:
1/1 ohm = 1/R1 + 1/R2
1 = R1 + R2 ...........(2)
Now, we have two equations (equation 1 and equation 2) with two unknowns (R1 and R2). We can solve these equations simultaneously to find the values of R1 and R2.
To do this, subtract equation 2 from equation 1:
4.5 ohms - 1 = (R1 + R2) - (R1 + R2)
3.5 ohms = 0
Since 3.5 ohms is not equal to 0, this implies that the given set of resistances (R1 and R2) does not satisfy the conditions mentioned in the problem.
However, the answer options mention two resistance values that do satisfy the conditions. Let's check option C: 1.5 ohms and 3 ohms.
Checking in series: 1.5 ohms + 3 ohms = 4.5 ohms (satisfying the condition)
Checking in parallel: 1/(1.5 ohms) + 1/(3 ohms) = 1 ohm (satisfying the condition)
Hence, the correct answer is option C: 1.5 ohms and 3 ohms.
Resistance in series: R_series = 4.5 ohms
Resistance in parallel: R_parallel = 1 ohm
To find:
The resistance values of R1 and R2.
Solution:
Let's start by calculating the resistance in series. When two resistances are connected in series, their resistances add up.
Resistance in series:
R_series = R1 + R2
Substituting the given value, we get:
4.5 ohms = R1 + R2 ...........(1)
Next, let's calculate the resistance in parallel. When two resistances are connected in parallel, their reciprocal values add up, and the sum is the reciprocal of the total resistance.
Resistance in parallel:
1/R_parallel = 1/R1 + 1/R2
Substituting the given value, we get:
1/1 ohm = 1/R1 + 1/R2
1 = R1 + R2 ...........(2)
Now, we have two equations (equation 1 and equation 2) with two unknowns (R1 and R2). We can solve these equations simultaneously to find the values of R1 and R2.
To do this, subtract equation 2 from equation 1:
4.5 ohms - 1 = (R1 + R2) - (R1 + R2)
3.5 ohms = 0
Since 3.5 ohms is not equal to 0, this implies that the given set of resistances (R1 and R2) does not satisfy the conditions mentioned in the problem.
However, the answer options mention two resistance values that do satisfy the conditions. Let's check option C: 1.5 ohms and 3 ohms.
Checking in series: 1.5 ohms + 3 ohms = 4.5 ohms (satisfying the condition)
Checking in parallel: 1/(1.5 ohms) + 1/(3 ohms) = 1 ohm (satisfying the condition)
Hence, the correct answer is option C: 1.5 ohms and 3 ohms.
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Two resistances R1 and R2 give combined resistance of 4.5 ohms when in series and 1 ohm when in parallel. The resistance area)3 ohms and 6 ohmsb)3 ohms and 9 ohmsc)1.5 ohms and 3 ohmsd)1.5 ohms and 0.5 ohmsCorrect answer is option 'C'. Can you explain this answer?
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