`6Omega` and `12Omega` resistors are connected in parallel. This combination is connected in series with 10 V battery and `6 Omega` resistor. What is the potential differnce between the terminals of the `12Omega` resistor ?

Options

A. 4 V
B. 16 V
C. 2
D. 8 V

Answer

To solve the problem step by step, we will follow the outlined process in the video transcript and add some explanations along the way.

### Step 1: Understand the Circuit Configuration
We have a `6Ω` resistor and a `12Ω` resistor connected in parallel. This parallel combination is connected in series with a `6Ω` resistor and a `10V` battery.

### Step 2: Draw the Circuit
The circuit can be represented as follows:
- Connect the `10V` battery to a `6Ω` resistor (let's call this R1).
- From the other end of R1, connect the parallel combination of the `6Ω` (let's call this R2) and `12Ω` (let's call this R3) resistors.

### Step 3: Calculate the Equivalent Resistance of the Parallel Combination
The equivalent resistance \( R_{XY} \) of the `6Ω` and `12Ω` resistors in parallel can be calculated using the formula:
\[ \frac{1}{R_{XY}} = \frac{1}{R_2} + \frac{1}{R_3} \]
Substituting the values:
\[ \frac{1}{R_{XY}} = \frac{1}{6} + \frac{1}{12} \]
Finding a common denominator (which is 12):
\[ \frac{1}{R_{XY}} = \frac{2}{12} + \frac{1}{12} = \frac{3}{12} = \frac{1}{4} \]
Thus, the equivalent resistance \( R_{XY} \) is:
\[ R_{XY} = 4Ω \]

### Step 4: Calculate the Total Resistance in the Circuit
The total resistance \( R_{total} \) in the circuit is the sum of the series resistances:
\[ R_{total} = R_1 + R_{XY} = 6Ω + 4Ω = 10Ω \]

### Step 5: Calculate the Total Current in the Circuit
Using Ohm's Law, the current \( I \) in the circuit can be calculated as:
\[ I = \frac{V}{R_{total}} = \frac{10V}{10Ω} = 1A \]

### Step 6: Calculate the Voltage Across the Parallel Combination
The voltage across the parallel combination (which is also the voltage across the `6Ω` and `12Ω` resistors) can be calculated using Ohm's Law:
\[ V_{XY} = I \times R_{XY} = 1A \times 4Ω = 4V \]

### Step 7: Conclusion
Thus, the potential difference between the terminals of the `12Ω` resistor is **4V**.

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