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
\(\frac{5 \,E}{5\, R+r}=\frac{5 \,E}{5\, r+R}\)
\(5\, R+r=5 \,r+R\)
\(4 \,R=4 \,r \Rightarrow \frac{R}{r}=\frac{4}{4}\)
\(\frac{R}{r}=1\)
Top Questions on Current electricity
- Find the equivalent resistance between two ends of the following circuit:
- JEE Main - 2025
- Physics
- Current electricity
Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R):
Assertion (A): In an insulated container, a gas is adiabatically shrunk to half of its initial volume. The temperature of the gas decreases.
Reason (R): Free expansion of an ideal gas is an irreversible and an adiabatic process.In the light of the above statements, choose the correct answer from the options given below:
- JEE Main - 2025
- Physics
- Current electricity
- Two conductors A and B of the same material have their lengths in the ratio 1:2 and radii in the ratio 2:3. If they are connected in parallel across a battery, the ratio \( \frac{v_A}{v_B} \) of the drift velocities of electrons in them will be:
- CBSE CLASS XII - 2025
- Physics
- Current electricity
- A conductor of length \( l \) is connected across an ideal cell of emf E. Keeping the cell connected, the length of the conductor is increased to \( 2l \) by gradually stretching it. If R and \( R' \) are initial and final values of resistance and \( v_d \) and \( v_d' \) are initial and final values of drift velocity, find the relation between:
\( R' \) and \( R \)
\( R' = 4R \)- CBSE CLASS XII - 2025
- Physics
- Current electricity
- \( n \) identical cells, each of e.m.f \( E \) and internal resistance \( r \), are connected in series. Later on, it was found that two cells ‘X’ and ‘Y’ are connected in reverse polarities. Calculate the potential difference across the cell ‘X’.
- CBSE CLASS XII - 2025
- Physics
- Current electricity
Questions Asked in KEAM exam
- If the lines \( \frac{x-1}{2} = \frac{y-2}{\alpha} = \frac{z-3}{2} \) and \( \frac{x-1}{2} = \frac{y-2}{1} = \frac{z-3}{-2} \) are perpendicular, then the value of \( \alpha \) is:
- KEAM - 2024
- Integration
- If \( \alpha, \beta, \gamma \) are the angles made by $$ \frac{x-1}{3} = \frac{y+1}{2} = -\frac{z}{1} \text{ with the coordinate axes, then } $$ \((\cos\alpha, \cos\beta, \cos\gamma) = \)
- KEAM - 2024
- Multiplication of a Vector by a Scalar
- Evaluate the limit: $$ \lim_{x \to 4} \left( \frac{1}{x - 4} - \frac{5}{x^2 - 3x - 4} \right) $$ is equal to
- KEAM - 2024
- Limit and Continuity
- In a combustion reaction, heat change during the formation of 40 g of carbon dioxide from carbon and dioxygen gas is (Enthalpy of combustion of carbon = -396 kJ mol\(^1\))
- KEAM - 2024
- Thermodynamics
- In the measurement of length 6 $\mu$m is equal to $x$ pm. Then the value of $x$ is
- KEAM - 2024
- Dimensional Analysis
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.