Three conductors draw respectively currents of 1 A, 2 A and 4 A when connected in turn across a battery. If they are connected in series across the same battery, the current drawn will be

Options

A. `(2)/(7) A`
B. `(3)/(7) A`
C. `(4)/(7) A`
D. `(5)/(7) A`

Explanation

To solve the problem of finding the current drawn when three conductors are connected in series across a battery, we can follow these steps:

### Step 1: Understand the Problem
We have three conductors that draw different currents when connected individually to a battery. The currents are:
- Conductor 1: 1 A
- Conductor 2: 2 A
- Conductor 3: 4 A

When these conductors are connected in series, we need to find the total current drawn from the battery.

### Step 2: Apply Ohm's Law
According to Ohm's Law, the relationship between voltage (V), current (I), and resistance (R) is given by:
\[ V = I \cdot R \]
From this, we can express resistance as:
\[ R = \frac{V}{I} \]

### Step 3: Calculate Individual Resistances
Using the above formula, we can calculate the resistance of each conductor when they are connected to the same battery voltage (V):
- Resistance of Conductor 1 (R1):
\[ R_1 = \frac{V}{1} = V \]
- Resistance of Conductor 2 (R2):
\[ R_2 = \frac{V}{2} = \frac{V}{2} \]
- Resistance of Conductor 3 (R3):
\[ R_3 = \frac{V}{4} = \frac{V}{4} \]

### Step 4: Calculate Total Resistance in Series
When resistors are connected in series, the total resistance (R_total) is the sum of individual resistances:
\[ R_{\text{total}} = R_1 + R_2 + R_3 \]
Substituting the values we calculated:
\[ R_{\text{total}} = V + \frac{V}{2} + \frac{V}{4} \]

### Step 5: Simplify the Total Resistance
To simplify this, we can express all terms with a common denominator:
- The common denominator for 1, 2, and 4 is 4:
\[ R_{\text{total}} = \frac{4V}{4} + \frac{2V}{4} + \frac{V}{4} = \frac{4V + 2V + V}{4} = \frac{7V}{4} \]

### Step 6: Calculate the Current in Series
Now, we can find the current (I) when the conductors are connected in series using Ohm's Law:
\[ I = \frac{V}{R_{\text{total}}} \]
Substituting the expression for total resistance:
\[ I = \frac{V}{\frac{7V}{4}} \]
This simplifies to:
\[ I = \frac{V \cdot 4}{7V} = \frac{4}{7} \]

### Final Answer
Thus, the total current drawn when the conductors are connected in series across the battery is:
\[ \boxed{\frac{4}{7} \text{ A}} \]