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Analyse the given electric circuit and answer the network: i) The equivalent resistance of the network T ii) The total electric current I in the circuit

Physics

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Answers

2 parts
i

C) 20Ω\text{C) } 20 \Omega

ii

C) 0.15 A\text{C) } 0.15 \text{ A}

Step-by-step solution

8 steps

Here's the analysis of the given electric circuit:

Part i· 4 steps

The equivalent resistance of the network

  1. Identify the resistors and their connection.

    The circuit shows two resistors, R1=60ΩR_1 = 60 \Omega and R2=30ΩR_2 = 30 \Omega, connected in parallel.

  2. Calculate the equivalent resistance (ReqR_{eq}) for parallel resistors.

    The formula for two resistors in parallel is:

    Req=R1R2R1+R2R_{eq} = \frac{R_1 R_2}{R_1 + R_2}
  3. Substitute the values and calculate the equivalent resistance.

    Req=60Ω×30Ω60Ω+30ΩR_{eq} = \frac{60 \Omega \times 30 \Omega}{60 \Omega + 30 \Omega} Req=1800Ω290ΩR_{eq} = \frac{1800 \Omega^2}{90 \Omega} Req=20ΩR_{eq} = 20 \Omega
  4. Select the correct option.

    Comparing with the given options: A) 30Ω30 \Omega, B) 60Ω60 \Omega, C) 20Ω20 \Omega, D) 90Ω90 \Omega.
    The correct option is C) 20Ω\boxed{\text{C) } 20 \Omega}.

Part ii

C) 0.15 A\text{C) } 0.15 \text{ A}

The total electric current I in the circuit

  1. Identify the total voltage and equivalent resistance.

    The dry cell provides a voltage V=3 VV = 3 \text{ V}.
    The equivalent resistance of the circuit is Req=20ΩR_{eq} = 20 \Omega (calculated in part i).

  2. Apply Ohm's Law to find the total current.

    Ohm's Law states I=VReqI = \frac{V}{R_{eq}}.

  3. Substitute the values and calculate the total current.

    I=3 V20ΩI = \frac{3 \text{ V}}{20 \Omega} I=0.15 AI = 0.15 \text{ A}
  4. Select the correct option.

    Comparing with the given options: A) 0.1 A0.1 \text{ A}, B) 0.05 A0.05 \text{ A}, C) 0.15 A0.15 \text{ A}, D) 0.00 A0.00 \text{ A}.
    The correct option is C) 0.15 A\boxed{\text{C) } 0.15 \text{ A}}.

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