Five cells each of emf $E$ and internal resistance $r$ send the same amount of current through an external resistance $R$ whether the cells are connected in parallel or in series. Then the ratio $\left( \frac{R}{r} \right)$ is
- 2
- $\frac{1}{2}$
- $\frac{1}{5}$
- 1
The Correct Option is D
Solution and Explanation
The correct option is(D): 1
When \(5\) cell are joined in parallel as shown,
\(i=\frac{\text { net emf }}{\text { total resistance }}\)
\(i=\frac{5 \,E}{5 \,R+r}\)
When \(5\) cell are joined in series as shown,
\(i=\frac{5\, E}{5\, r+R}\)
So, according to the questions
\(\frac{5 \,E}{5\, R+r}=\frac{5 \,E}{5\, r+R}\)
\(5\, R+r=5 \,r+R\)
\(4 \,R=4 \,r \Rightarrow \frac{R}{r}=\frac{4}{4}\)
\(\frac{R}{r}=1\)
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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.