Four resistances of 16 ohms each are connected in parallel. Four such combinations are connected in series. What is the total resistance?

Answer

To solve the problem of finding the total resistance when four resistances of 16 ohms each are connected in parallel, and then four such combinations are connected in series, we can follow these steps:

### Step 1: Calculate the equivalent resistance of the parallel combination
When resistors are connected in parallel, the formula to find the equivalent resistance \( R_p \) is given by:

\[ \frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \frac{1}{R_4} \]

In this case, all resistances \( R_1, R_2, R_3, R_4 \) are equal to 16 ohms.

\[ \frac{1}{R_p} = \frac{1}{16} + \frac{1}{16} + \frac{1}{16} + \frac{1}{16} \]

### Step 2: Simplify the equation
Since there are four resistances of 16 ohms each, we can simplify:

\[ \frac{1}{R_p} = \frac{4}{16} = \frac{1}{4} \]

### Step 3: Find the equivalent resistance of the parallel combination
Now, we take the reciprocal to find \( R_p \):

\[ R_p = 4 \, \text{ohms} \]

### Step 4: Calculate the total resistance for the series combination
Now, since there are four such parallel combinations connected in series, the total resistance \( R_t \) is the sum of the individual resistances:

\[ R_t = R_p + R_p + R_p + R_p = 4 + 4 + 4 + 4 \]

### Step 5: Simplify the total resistance
Calculating this gives:

\[ R_t = 16 \, \text{ohms} \]

### Final Answer
The total resistance of the circuit is \( 16 \, \text{ohms} \).

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