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Calculate the equivalent resistance (R_p) of the two parallel resistors.

Physics

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Answer

16.15 A\text{16.15 A}

Step-by-step solution

3 steps
  1. Calculate the equivalent resistance (RpR_p) of the two parallel resistors.

    The 4 Ω4 \text{ } \Omega and 3 Ω3 \text{ } \Omega resistors are in parallel.

    Rp=R1×R2R1+R2R_p = \frac{R_1 \times R_2}{R_1 + R_2} Rp=4 Ω×3 Ω4 Ω+3 ΩR_p = \frac{4 \text{ } \Omega \times 3 \text{ } \Omega}{4 \text{ } \Omega + 3 \text{ } \Omega} Rp=12 Ω27 ΩR_p = \frac{12 \text{ } \Omega^2}{7 \text{ } \Omega} Rp≈1.714 ΩR_p \approx 1.714 \text{ } \Omega
  2. Calculate the total equivalent resistance (RtotalR_{total}) of the circuit.

    The parallel combination (RpR_p) is in series with the 2 Ω2 \text{ } \Omega resistor.

    Rtotal=Rp+RseriesR_{total} = R_p + R_{series} Rtotal=1.714 Ω+2 ΩR_{total} = 1.714 \text{ } \Omega + 2 \text{ } \Omega Rtotal=3.714 ΩR_{total} = 3.714 \text{ } \Omega
  3. Calculate the total electric current (II) using Ohm's Law.

    The voltage source is 60 V60 \text{ V}.

    I=VRtotalI = \frac{V}{R_{total}} I=60 V3.714 ΩI = \frac{60 \text{ V}}{3.714 \text{ } \Omega} I≈16.15 AI \approx 16.15 \text{ A}

    The total electric current is 16.15 A\text{16.15 A}.

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