Question

(i) State Ohm's law. What will be the value of current and potential difference at the ends of each resistance in the given circuit?
\includegraphics[width=0.5\linewidth]{image1.png}

Hint:

In series circuits, the total resistance is the sum of individual resistances, and the current remains constant throughout all resistors.

Answer 1

Ohm's Law:
Ohm's Law states that the current (\(I\)) passing through a conductor between two points is directly proportional to the potential difference (\(V\)) across the two points and inversely proportional to the resistance (\(R\)) of the conductor. Mathematically, it is expressed as: \[ V = IR \] Where: - \(V\) is the potential difference (voltage) across the conductor,
- \(I\) is the current flowing through the conductor,
- \(R\) is the resistance of the conductor.
Given Circuit:
In the given circuit, three resistances of \(15 \, \Omega\) each are connected in series across a 10V battery. To find the current through the resistors and the potential difference across each, we first calculate the total resistance and then use Ohm's law.

Step 1: Total Resistance in Series
The total resistance in a series circuit is the sum of the individual resistances. Therefore, the total resistance (\(R_{\text{total}}\)) in this case is: \[ R_{\text{total}} = R_1 + R_2 + R_3 = 15 \, \Omega + 15 \, \Omega + 15 \, \Omega = 45 \, \Omega \]

Step 2: Current in the Circuit
Using Ohm's law, the current \(I\) in the circuit can be calculated using the formula: \[ I = \frac{V}{R_{\text{total}}} = \frac{10 \, \text{V}}{45 \, \Omega} = 0.222 \, \text{A} \] So, the current flowing through the entire circuit is approximately \(0.22 \, \text{A}\).

Step 3: Potential Difference Across Each Resistor
In a series circuit, the current through each resistor is the same. The potential difference across each resistor (\(V_{\text{R}}\)) can be calculated using Ohm's law: \[ V_{\text{R}} = I \times R \] Substituting the values: \[ V_{\text{R}} = 0.222 \, \text{A} \times 15 \, \Omega = 3.33 \, \text{V} \] So, the potential difference across each resistor is approximately \(3.33 \, \text{V}\).
Conclusion:
- The current through the circuit is \(0.22 \, \text{A}\).
- The potential difference across each resistance is \(3.33 \, \text{V}\).