Three cells each of emf, 1.0 V, and internal resistance, 2Ω, are connected in parallel

PHYSICSWAEC 2022

Three cells each of emf, 1.0 V, and internal resistance, 2Ω, are connected in parallel across a 3Ω resistor. Determine the current in the resistor.

  • A. 0.90A
  • B. 0.39A
  • C. 0.30A
  • D. 0.01A

Correct Answer: C. 0.30A

Explanation

Given Data: Emf = 1v, r = 2 ohms, R = 3 ohms, I = ?

3 resistance in parallel = \(\frac{1}{r_1}\) + \(\frac{1}{r_2}\) + \(\frac{1}{r_3}\)

\(\frac{1}{r_T}\)= \(\frac{1}{2}\) + \(\frac{1}{2}\) + \(\frac{1}{2}\)

\(\frac{1}{r_T}\) = \(\frac{1+1+1}{2}\)

\(\frac{1}{r_T}\) = \(\frac{3}{2}\)

cross multiply

r\(_T\) = \(\frac{2}{3}\) or 0.67

E = I(R+r)

1 = I(3+0.67)

1 = I(3.67)

1 ÷ 3.67 = I

0.27 = I

: I ≈ 0.30A

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