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AP EAMCET · PHYSICS · Current Electricity

When two identical batteries of internal resistance \(1 \Omega\) each are connected in series across a resistor \(R\), the rate of heat produced in \(R\) is \(P_1\). When the same batteries are connected in parallel across \(R\), the rate of heat produced is \(P_2\). If \(\mathrm{P}_1=2.25 \mathrm{P}_2\), then the value of R is

  1. A \(2 \Omega\)
  2. B \(4 \Omega\)
  3. C \(10 \Omega\)
  4. D \(12 \Omega\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(4 \Omega\)

Step-by-step Solution

Detailed explanation

For series connection: \(E_s = 2E\) \(r_s = 2r = 2(1) = 2 \, \Omega\) \(I_1 = \frac{2E}{R+2}\) \(P_1 = I_1^2 R = \left(\frac{2E}{R+2}\right)^2 R\) For parallel connection: \(E_p = E\) \(r_p = \frac{r}{2} = \frac{1}{2} \, \Omega\) \(I_2 = \frac{E}{R+\frac{1}{2}}\)…