A potential difference of 10V is applied across a conductor of conductance 5Ω-1. The current through the conductor is :
50A
Understanding Current, Voltage, and Conductance
This question asks us to find the current flowing through a conductor when a specific potential difference is applied across it and its conductance is known. This involves understanding the relationship between current, voltage, and the electrical properties of the conductor.
We are given the following information:
- Potential difference (Voltage), \(V = 10V\)
- Conductance, \(G = 5\Omega^{-1}\)
We need to find the current, \(I\).
Relating Current, Voltage, and Conductance
Ohm's Law gives us the fundamental relationship between voltage, current, and resistance: \(V = IR\), where R is the resistance.
Conductance (\(G\)) is a measure of how easily electric current flows through a material. It is the reciprocal of resistance (\(R\)). Mathematically, this relationship is expressed as:
\(G = \frac{1}{R}\)
We can substitute the relationship between conductance and resistance into Ohm's Law to find a formula that directly relates current, voltage, and conductance.
From Ohm's Law, \(R = \frac{V}{I}\).
Substituting this into the conductance formula:
\(G = \frac{1}{\frac{V}{I}}\)
\(G = \frac{I}{V}\)
Rearranging this formula to solve for the current (\(I\)):
\(I = V \times G\)
This formula allows us to calculate the current directly from the potential difference (voltage) and the conductance.
Calculating the Current
Now, we can plug in the given values for voltage (\(V\)) and conductance (\(G\)) into the derived formula \(I = V \times G\).
\(I = 10V \times 5\Omega^{-1}\)
\(I = 50 A\)
Therefore, the current through the conductor is 50 Amperes.
Step-by-Step Calculation Summary
- Identify the given values: Voltage \(V = 10V\), Conductance \(G = 5\Omega^{-1}\).
- Recall the relationship between current, voltage, and conductance: \(I = V \times G\).
- Substitute the given values into the formula: \(I = 10 \times 5\).
- Calculate the result: \(I = 50\).
- State the unit for current, which is Amperes (A).
Final Answer
The current through the conductor is 50A.
| Quantity | Symbol | Value | Unit |
|---|---|---|---|
| Potential Difference | \(V\) | 10 | \(V\) (Volts) |
| Conductance | \(G\) | 5 | \(\Omega^{-1}\) or \(S\) (Siemens) |
| Current | \(I\) | Calculated (50) | \(A\) (Amperes) |
Revision Table: Electrical Concepts
| Concept | Symbol | Definition | Units | Relation to Ohm's Law |
|---|---|---|---|---|
| Potential Difference (Voltage) | \(V\) | Energy per unit charge between two points. | Volts (V) | \(V = IR\) |
| Current | \(I\) | Rate of flow of electric charge. | Amperes (A) | \(I = V/R\) or \(I = VG\) |
| Resistance | \(R\) | Opposition to the flow of electric current. | Ohms (\(\Omega\)) | \(R = V/I\) or \(R = 1/G\) |
| Conductance | \(G\) | Ease with which electric current flows. | Siemens (S) or \(\Omega^{-1}\) | \(G = 1/R\) or \(G = I/V\) |
Additional Information: Electrical Conductance
Conductance is an important property in electrical circuits. High conductance means the material allows current to flow easily, while low conductance means it resists current flow. It is the reciprocal of resistance. The unit for conductance is the Siemens (S), named after Werner von Siemens. One Siemens is equal to one \(\Omega^{-1}\). The formula \(I = V \times G\) is particularly useful when working directly with conductance instead of resistance. This relationship is a direct consequence of Ohm's law and the definition of conductance.
Important Questions from Resistance and Resistivity
If the length of a conductor is doubled, then the resistance of the conductor will be: (other parameters are kept same)
Which factor does NOT affect the resistivity of a material?
Based on the English alphabetical order, three of the following four letter-clusters are alike in a certain way and thus form a group. Which letter-cluster does not belong to that group?
(Note: The odd one out is not based on the number of consonants/vowels or their position in the letter-cluster.)
In a circuit, a 10-volt battery and three resistors ( R1 = 2 Ω ), ( R2 = 3 Ω), and ( R3 = 6 Ω) are connected in parallel to each other. Which of the following is the correct value of effective resistance ( Re ) and current I flowing through the circuit?
A uniform wire of resistance 9Ω is bent in the form of an equilateral triangle. Find the effective resistance across a side of the triangle.
