The conductivity of four electrolytes P, Q, R, S in `ohm^(-1) cm^(-1)` area as follows `P (5 xx 10^(-6)), Q (1 xx 10^(-10)), R (7 xx 10^(-8)), S(9.2 xx 10^(-3))`. The one which offers highest resistance to the passage of electric current is

Options

A. P
B. S
C. R
D. Q

Answer

To determine which electrolyte offers the highest resistance to the passage of electric current, we can follow these steps:

### Step 1: Understand the relationship between conductivity and resistance
The relationship between conductivity (K) and resistance (R) is given by the formula:
\[ R = \frac{1}{K} \]
where:
- \( R \) is the resistance in ohms (Ω),
- \( K \) is the conductivity in ohm\(^{-1}\) cm\(^{-1}\).

### Step 2: List the conductivities of the electrolytes
We have the following conductivities for the electrolytes:
- \( K_P = 5 \times 10^{-6} \) ohm\(^{-1}\) cm\(^{-1}\)
- \( K_Q = 1 \times 10^{-10} \) ohm\(^{-1}\) cm\(^{-1}\)
- \( K_R = 7 \times 10^{-8} \) ohm\(^{-1}\) cm\(^{-1}\)
- \( K_S = 9.2 \times 10^{-3} \) ohm\(^{-1}\) cm\(^{-1}\)

### Step 3: Calculate the resistance for each electrolyte
Now we will calculate the resistance for each electrolyte using the formula \( R = \frac{1}{K} \).

1. **For electrolyte P:**
\[ R_P = \frac{1}{5 \times 10^{-6}} = 2 \times 10^{5} \, \text{Ω} \]

2. **For electrolyte Q:**
\[ R_Q = \frac{1}{1 \times 10^{-10}} = 1 \times 10^{10} \, \text{Ω} \]

3. **For electrolyte R:**
\[ R_R = \frac{1}{7 \times 10^{-8}} \approx 1.4286 \times 10^{7} \, \text{Ω} \]

4. **For electrolyte S:**
\[ R_S = \frac{1}{9.2 \times 10^{-3}} \approx 108.7 \, \text{Ω} \]

### Step 4: Compare the resistances
Now we compare the calculated resistances:
- \( R_P = 2 \times 10^{5} \, \text{Ω} \)
- \( R_Q = 1 \times 10^{10} \, \text{Ω} \)
- \( R_R \approx 1.4286 \times 10^{7} \, \text{Ω} \)
- \( R_S \approx 108.7 \, \text{Ω} \)

### Step 5: Identify the highest resistance
From the calculated values, we can see that:
- The highest resistance is \( R_Q = 1 \times 10^{10} \, \text{Ω} \).

### Conclusion
Therefore, the electrolyte that offers the highest resistance to the passage of electric current is **Q**.

---