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Calculate the total equivalent resistance of the circuit.

Physics

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Answer

235 Ω\text{235 } \Omega

Step-by-step solution

3 steps
  1. Identify the parallel resistors.

    The two 60 Ω60 \, \Omega resistors are connected in parallel. Calculate their equivalent resistance, RpR_p.

    Rp=R1×R2R1+R2R_p = \frac{R_1 \times R_2}{R_1 + R_2} Rp=60 Ω×60 Ω60 Ω+60 ΩR_p = \frac{60 \, \Omega \times 60 \, \Omega}{60 \, \Omega + 60 \, \Omega} Rp=3600 Ω2120 ΩR_p = \frac{3600 \, \Omega^2}{120 \, \Omega} Rp=30 ΩR_p = 30 \, \Omega
  2. Identify the series resistors.

    The 180 Ω180 \, \Omega resistor is in series with the equivalent resistance RpR_p. Let's call this combination RsR_s.

    Rs=180 Ω+RpR_s = 180 \, \Omega + R_p Rs=180 Ω+30 ΩR_s = 180 \, \Omega + 30 \, \Omega Rs=210 ΩR_s = 210 \, \Omega
  3. Calculate the total equivalent resistance, RTR_T.

    The 25 Ω25 \, \Omega resistor is in series with RsR_s.

    RT=25 Ω+RsR_T = 25 \, \Omega + R_s RT=25 Ω+210 ΩR_T = 25 \, \Omega + 210 \, \Omega RT=235 ΩR_T = 235 \, \Omega

    The total equivalent resistance is 235 Ω\text{235 } \Omega.

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