In a potentiometer circuit a cell of EMF $1.5\, V$ gives balance point at $36\, cm$ length of wire. If another cell of EMF $2.5\, V$ replaces the first cell, then at what length of the wire, the balance point occurs ?
- 60 cm
- 21.6 cm
- 64 cm
- 62 cm
The Correct Option is A
Solution and Explanation
To solve this problem, we need to understand the principle of a potentiometer. A potentiometer is used to measure the electromotive force (EMF) of a cell by balancing it against a known potential difference. The balancing length (or null point) of the wire in the potentiometer setup is proportional to the EMF of the cell connected.
Let's analyze the given data and solve step-by-step:
- The balance point for the first cell with an EMF of \(1.5\, V\) occurs at a wire length of \(36\, cm\). According to the principle of the potentiometer, the balance condition is given by: \(E_1 \propto L_1\), where \(E_1 = 1.5\, V\) and \(L_1 = 36\, cm\).
- Now, if another cell with an EMF of \(2.5\, V\) replaces the first cell, we need to find the new balance length \(L_2\).
- Using the direct proportionality \(\frac{E_1}{E_2} = \frac{L_1}{L_2}\), the equation can be rearranged to solve for \(L_2\): \(L_2 = \frac{E_2 \cdot L_1}{E_1}\).
- Substitute the values: \(L_2 = \frac{2.5\, V \cdot 36\, cm}{1.5\, V} = \frac{90\, cm}{1.5}\).
- This simplifies to: \(L_2 = 60\, cm\).
Therefore, the balance point for the second cell with an EMF of \(2.5\, V\) occurs at \(60\, cm\) of the wire.
The correct option is: 60 cm.
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Concepts Used:
Current Electricity
Current electricity is defined as the flow of electrons from one section of the circuit to another.
Types of Current Electricity
There are two types of current electricity as follows:
Direct Current
The current electricity whose direction remains the same is known as direct current. Direct current is defined by the constant flow of electrons from a region of high electron density to a region of low electron density. DC is used in many household appliances and applications that involve a battery.
Alternating Current
The current electricity that is bidirectional and keeps changing the direction of the charge flow is known as alternating current. The bi-directionality is caused by a sinusoidally varying current and voltage that reverses directions, creating a periodic back-and-forth motion for the current. The electrical outlets at our homes and industries are supplied with alternating current.