A student has 10 resistors of resistance ‘ r ’. The minimum resistance made by him from given resistors is

Options

A. 10r
B. `(r)/(10)`
C. `(r)/(100)`
D. `(r)/(5)`

Answer

To find the minimum resistance that can be made using 10 resistors, each with a resistance of \( r \), we will connect all the resistors in parallel. Here’s a step-by-step solution:

### Step 1: Understanding Resistance in Parallel
When resistors are connected in parallel, the formula for the equivalent resistance \( R_{eq} \) is given by:

\[ \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \ldots + \frac{1}{R_n} \]

### Step 2: Applying the Formula
Since all 10 resistors have the same resistance \( r \), we can denote the resistance of each resistor as \( R_1 = R_2 = \ldots = R_{10} = r \). Therefore, we can rewrite the equation for the equivalent resistance as:

\[ \frac{1}{R_{eq}} = \frac{1}{r} + \frac{1}{r} + \frac{1}{r} + \ldots + \frac{1}{r} \quad (\text{10 times}) \]

### Step 3: Simplifying the Equation
This simplifies to:

\[ \frac{1}{R_{eq}} = \frac{10}{r} \]

### Step 4: Finding the Equivalent Resistance
To find \( R_{eq} \), we take the reciprocal of both sides:

\[ R_{eq} = \frac{r}{10} \]

### Conclusion
Thus, the minimum resistance that can be obtained by connecting all 10 resistors in parallel is:

\[ \boxed{\frac{r}{10}} \]