In post office box experiment `Q/P=1/10.` In `R` if 142 `Omega` is used then we get deflection towards right and if `R=143 Omega`, then deflection is towards left. What is the range of unknown resistance?

Explanation

To solve the problem, we will follow these steps:

### Step 1: Understand the relationship between Q, P, and R
In the post office box experiment, we are given that \( \frac{Q}{P} = \frac{1}{10} \). This implies that \( \frac{P}{Q} = 10 \).

### Step 2: Apply the formula from the experiment
According to the post office box experiment, we have the relationship:
\[ \frac{P}{Q} = \frac{R}{X} \]
where \( R \) is the known resistance and \( X \) is the unknown resistance.

### Step 3: Substitute the value of \( P/Q \)
From Step 1, we substitute \( \frac{P}{Q} = 10 \) into the equation:
\[ 10 = \frac{R}{X} \]

### Step 4: Rearrange the equation to find \( X \)
Rearranging the equation gives us:
\[ X = \frac{R}{10} \]

### Step 5: Calculate \( X \) for \( R = 142 \, \Omega \)
Substituting \( R = 142 \, \Omega \) into the equation:
\[ X = \frac{142}{10} = 14.2 \, \Omega \]

### Step 6: Calculate \( X \) for \( R = 143 \, \Omega \)
Now substituting \( R = 143 \, \Omega \):
\[ X = \frac{143}{10} = 14.3 \, \Omega \]

### Step 7: Determine the range of unknown resistance \( X \)
From the calculations in Steps 5 and 6, we find that the unknown resistance \( X \) ranges from:
\[ 14.2 \, \Omega \text{ to } 14.3 \, \Omega \]

### Final Answer
The range of the unknown resistance \( X \) is:
\[ 14.2 \, \Omega \leq X \leq 14.3 \, \Omega \]

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