Question:
In order to measure the internal resistance r1 of a cell of emf E, a meter bridge of wire resistance R0 = 50 Ω, a resistance \(\frac{R_0}{2}\), another cell of emf \(\frac{E}{2}\) (internal resistance r) and a galvanometer G are used in a circuit, as shown in the figure. If the null point is found at l = 72 cm, then the value of r 1 = ____
In order to measure the internal resistance r1 of a cell of emf E, a meter bridge of wire resistance R0 = 50 Ω, a resistance \(\frac{R_0}{2}\), another cell of emf \(\frac{E}{2}\) (internal resistance r) and a galvanometer G are used in a circuit, as shown in the figure. If the null point is found at l = 72 cm, then the value of r 1 = ____
Updated On: May 25, 2024
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Correct Answer: 3
Solution and Explanation
Current will flow in the main circuit
\(\begin{array}{l}I = \frac{E}{r_{1}+\frac{3R_{0}}{2}}\end{array}\)
\(\begin{array}{l}+E- IR_{0}\times 0.72-Ir_{1}-\frac{E}{2}=0\end{array}\)
\(\begin{array}{l}\frac{E}{2}=\frac{2E}{2r_{1}+3R_{0}}\times [0.72R_{0}+r_{1}]\end{array}\)
\(\begin{array}{l}2r_{1}+3R_{0}= 4[0.72R_{0}+r_{1}]\end{array}\)
0.12R0 = 2r1
r1 = 3Ω
\(\begin{array}{l}I = \frac{E}{r_{1}+\frac{3R_{0}}{2}}\end{array}\)
\(\begin{array}{l}+E- IR_{0}\times 0.72-Ir_{1}-\frac{E}{2}=0\end{array}\)
\(\begin{array}{l}\frac{E}{2}=\frac{2E}{2r_{1}+3R_{0}}\times [0.72R_{0}+r_{1}]\end{array}\)
\(\begin{array}{l}2r_{1}+3R_{0}= 4[0.72R_{0}+r_{1}]\end{array}\)
0.12R0 = 2r1
r1 = 3Ω
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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.
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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.