Four identical cells, each with internal resistance 1 \(\Omega\) and emf 10 V are connected in series to a resistance R and they are connected in parallel and then to an external resistance R in series. For what value of R the current in series and in parallel combination is the same?
Show Hint
- \(1 \, \Omega\)
- \(4 \, \Omega\)
- \(2 \, \Omega\)
- \(6 \, \Omega\)
The Correct Option is A
Solution and Explanation
\[ \text{Total emf (E)} = 4 \times 10 \, \text{V} = 40 \, \text{V} \] \[ \text{Total resistance (R)} = 4 \times 1 \, \Omega + R = 4 \, \Omega + R \]
Step 2: Calculate the total emf and resistance in parallel.For parallel, the total resistance of the batteries alone: \[ \frac{1}{R_{\text{total}}} = \frac{1}{1} + \frac{1}{1} + \frac{1}{1} + \frac{1}{1} = 4 \] \[ R_{\text{total}} = 0.25 \, \Omega \] Total resistance with external \( R \): \[ R_{\text{parallel}} = 0.25 \, \Omega + R \]
Step 3: Set the currents equal for series and parallel circuits.\[ \frac{40}{4+R} = \frac{10}{0.25+R} \] Solving for \( R \), \[ R = 1 \, \Omega \]
Top AP EAMCET Physics Questions
- If only $\frac{1}{51}^{th}$ ot the main current is to be passed through a galvanometer then the shunt required is $R_1$ and if only $\frac{1}{11}^{th}$ of the main voltage is to be developed across the galvanometer, then the resistance required is $R_2$. Then $\frac{R_2}{R_1} =$
In the given circuit, the electric currents through $15\, \Omega$ and $6 \, \Omega$ respectively are
- In a nuclear reactor the activity of a radioactive substance is $2000 / s$. If the mean life of the products is $50$ minutes, then in the steady power generation, the number of radio nuclides is
- In a $p$ - type semiconductor the donor level is at $50 \,meV$ above the valence band. To produce one electron, the maximum wavelength of light photon required is (Planck's constant, $h=6.6 \times 10^{-34} \,Js$ and speed of light in vacuum, $c=3 \times 10^{8} \,ms ^{-1}$ )
- Potential energy of a body of mass $1\, kg$ free to move along X-axis is given by $U(x) = \left( \frac{x^2}{2} - x \right) J .$ If the total mechanical energy of the body is $2\, J$. then the maximum speed of the body is (Assume only conservative force acts on the body)
Top AP EAMCET Electrical Instruments Questions
- If only $\frac{1}{51}^{th}$ ot the main current is to be passed through a galvanometer then the shunt required is $R_1$ and if only $\frac{1}{11}^{th}$ of the main voltage is to be developed across the galvanometer, then the resistance required is $R_2$. Then $\frac{R_2}{R_1} =$
In the given circuit, batteries are ideal and Galvanometer shows zero deflection, then the value of 'R' is:
The Wheatstone bridge is balanced when \(R_3 = 144 \, \Omega\). If \(R_2\) and \(R_1\) are interchanged, the bridge balances for \(R_3 = 169 \, \Omega\). The value of \(R_4\) is:
Top AP EAMCET Questions
- If $\int \cos x . \cos 2x . \cos 5x dx = A \; \sin 2x + B \sin 4x + C \sin 6x + D \sin 8x + k $ (where $k$ is the arbitrary constant of integration), then $\frac{1}{B} + \frac{1}{C} = $
- If $k$ is one of the roots of the equation $x^2 - 25x + 24 = 0 $ such that $A = \begin{bmatrix}1&2&1\\ 3&2&3\\ 1&1&k\end{bmatrix} $ is a non-singular matrix, then $A^{-1}$ =
- If only $\frac{1}{51}^{th}$ ot the main current is to be passed through a galvanometer then the shunt required is $R_1$ and if only $\frac{1}{11}^{th}$ of the main voltage is to be developed across the galvanometer, then the resistance required is $R_2$. Then $\frac{R_2}{R_1} =$
- If $p$ and $q$ are respectively the global maximum and global minimum of the function $f(x) = x^2 e^{2x}$ on the interval $[-2, 2]$ , then $pe^{-4} + qe^4 = $
- If $\displaystyle\sum^n_{k - 1} \tan^{-1} \left( \frac{1}{k^2 + k + 1} \right) = \tan^{-1} (\theta) $ , then $\theta$ =