Solve in English

English

ScanSolve AI Answer

Step-by-step solution

7 steps

Here is the solution to question 9:

9. (a) State the reading of the ammeter.

  1. Calculate the equivalent resistance of the parallel combination.

    The 6 Ω\Omega and 4 Ω\Omega resistors are in parallel.

    1Rp=16Ω+14Ω\frac{1}{R_p} = \frac{1}{6 \Omega} + \frac{1}{4 \Omega} 1Rp=212Ω+312Ω=512Ω\frac{1}{R_p} = \frac{2}{12 \Omega} + \frac{3}{12 \Omega} = \frac{5}{12 \Omega} Rp=125Ω=2.4ΩR_p = \frac{12}{5} \Omega = 2.4 \Omega
  2. Calculate the total effective resistance of the circuit.

    The parallel combination RpR_p is in series with the 2 Ω\Omega resistor.

    Rtotal=2Ω+Rp=2Ω+2.4Ω=4.4ΩR_{total} = 2 \Omega + R_p = 2 \Omega + 2.4 \Omega = 4.4 \Omega
  3. Calculate the total current (ammeter reading) using Ohm's Law.

    The total voltage is Vtotal=12 VV_{total} = 12 \text{ V}.

    Itotal=VtotalRtotal=12 V4.4Ω≈2.727 AI_{total} = \frac{V_{total}}{R_{total}} = \frac{12 \text{ V}}{4.4 \Omega} \approx 2.727 \text{ A}

    The reading of the ammeter is approximately 2.73 A\boxed{\text{2.73 A}}.

    9. (b) Calculate the effective resistance of the circuit.

  4. Calculate the equivalent resistance of the parallel combination (as in 9a, Step 1).

    Rp=2.4ΩR_p = 2.4 \Omega
  5. Calculate the total effective resistance of the circuit (as in 9a, Step 2).

    Rtotal=2Ω+Rp=2Ω+2.4Ω=4.4ΩR_{total} = 2 \Omega + R_p = 2 \Omega + 2.4 \Omega = 4.4 \Omega

    The effective resistance of the circuit is 4.4 Ω\boxed{\text{4.4 } \Omega}.

    9. (c) Calculate the potential difference across the 6 Ω\Omega resistor.

  6. Calculate the potential difference across the parallel combination.

    The potential difference across the 6 Ω\Omega resistor is the same as the potential difference across the parallel combination, VpV_p.

    Vp=Itotal×RpV_p = I_{total} \times R_p

    Using the more precise value for Itotal=124.4=3011 AI_{total} = \frac{12}{4.4} = \frac{30}{11} \text{ A}:

    Vp=3011 A×2.4Ω=3011×125 V=6×1211 V=7211 V≈6.545 VV_p = \frac{30}{11} \text{ A} \times 2.4 \Omega = \frac{30}{11} \times \frac{12}{5} \text{ V} = \frac{6 \times 12}{11} \text{ V} = \frac{72}{11} \text{ V} \approx 6.545 \text{ V}

    The potential difference across the 6 Ω\Omega resistor is approximately 6.55 V\boxed{\text{6.55 V}}.

    9. (d) Calculate the current flowing through the 4 Ω\Omega resistor.

  7. Use Ohm's Law for the 4 Ω\Omega resistor.

    The potential difference across the 4 Ω\Omega resistor is Vp=7211 VV_p = \frac{72}{11} \text{ V}.

    I4Ω=VpR4Ω=7211 V4Ω=7211×4 A=1811 A≈1.636 AI_{4\Omega} = \frac{V_p}{R_{4\Omega}} = \frac{\frac{72}{11} \text{ V}}{4 \Omega} = \frac{72}{11 \times 4} \text{ A} = \frac{18}{11} \text{ A} \approx 1.636 \text{ A}

    The current flowing through the 4 Ω\Omega resistor is approximately 1.64 A\boxed{\text{1.64 A}}.

Was this helpful?

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp