Three resistances of one ohm each are connected in parallel. Such connection is again connected with 2/3 resistor in series. The resultant resistance will bea)5/3 b)3/2 c)1 d)2/3 Correct answer is option 'C'. Can you explain this answer?

Question

Answer

R=R/n- for parallel resistor of n equal resistance
R=1/3 ohm. for resistor in parallel connection
R=2/3+1/3=1
HENCE R=1OHM IS THE RESULTANT RESISTANCE

Answer

Answer

**Given information:**
- Three resistances of 1 ohm each are connected in parallel.
- This parallel combination is connected with a resistor of 2/3 ohm in series.

**To find:**
The resultant resistance of the combination.

**Solution:**
To solve this problem, we will use the concept of equivalent resistance.

**Step 1:**
Let's find the equivalent resistance of the three resistances connected in parallel.

When resistances are connected in parallel, the reciprocal of the equivalent resistance is equal to the sum of the reciprocals of the individual resistances.

Let's represent the equivalent resistance of the parallel combination as Rp.

1/Rp = 1/R1 + 1/R2 + 1/R3

Since all three resistances are 1 ohm each,

1/Rp = 1/1 + 1/1 + 1/1
= 3/1
= 3 ohm

So, the equivalent resistance of the parallel combination is 3 ohms.

**Step 2:**
Now, the parallel combination is connected with a resistor of 2/3 ohm in series.

When resistances are connected in series, the equivalent resistance is simply the sum of the individual resistances.

Let's represent the equivalent resistance of the series combination as Rs.

Rs = Rp + R4
= 3 + 2/3
= (3*3 + 2)/3
= 11/3

So, the resultant resistance of the combination is 11/3 ohms.

**Step 3:**
Comparing the resultant resistance with the given options:

11/3 = 3.67

Option C: 1

Since 1 is not equal to 3.67, option C is incorrect.

Therefore, the correct answer is option A: 5/3.

**Conclusion:**
The resultant resistance of the combination is 11/3 ohms, which is equal to 3.67. So, the correct answer is option A: 5/3.

Answer

Opt c

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