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A perspex ruler is rubbed with a silk cloth, what charge will the ruler obtain? Resistors in series are __ dividers. An object that opposes the flow of current is a . Voltmeter measures the amount of

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6 parts
i

4.5 V4.5 \text{ V}

ii

1.5 V1.5 \text{ V}

iii

3 A3 \text{ A}

iv

6Ω6 \Omega

v

6 C6 \text{ C}

vi

18 J18 \text{ J}

Step-by-step solution

13 steps

Part 2

  • A perspex ruler is rubbed with a silk cloth, what charge will the ruler obtain?
    • Negative
  • Resistors in series are voltage dividers.
  • An object that opposes the flow of current resistor.
  • Voltmeter measures the amount of potential difference per charge.

Define the following terms:

  • Resistance: Resistance is the opposition to the flow of electric current in a circuit.
  • Series circuit: A series circuit is a circuit where components are connected end-to-end, forming a single path for the current to flow.

Part 3

Given:
Three 1.5 V1.5 \text{ V} cells in series, so total voltage E=3×1.5 V=4.5 V\mathcal{E} = 3 \times 1.5 \text{ V} = 4.5 \text{ V}.
A 2Ω2 \Omega resistor (under V1V_1) is in parallel with an unknown resistor.
The combined parallel resistance is 1.5Ω1.5 \Omega.
The reading on V4V_4 is 3 V3 \text{ V}.
The resistance under V4V_4 is 1Ω1 \Omega.

Part i

4.5 V4.5 \text{ V}

What is the reading on V5V_5?

  1. Identify V5V_5.

    V5V_5 measures the total voltage across the battery pack.

  2. Calculate the total voltage.

    There are three 1.5 V1.5 \text{ V} cells connected in series.

    V5=3×1.5 V=4.5 VV_5 = 3 \times 1.5 \text{ V} = 4.5 \text{ V}

    The reading on V5V_5 is 4.5 V\boxed{4.5 \text{ V}}.

Part ii

1.5 V1.5 \text{ V}

What is the reading on V1V_1?

  1. Understand the circuit.

    The 2Ω2 \Omega resistor and the unknown resistor are in parallel. This parallel combination is in series with the 1Ω1 \Omega resistor (under V4V_4). The ammeter A is in the main circuit. V1V_1 measures the voltage across the 2Ω2 \Omega resistor.

  2. Calculate the current through the 1Ω1 \Omega resistor.

    The reading on V4V_4 is 3 V3 \text{ V} and the resistance under V4V_4 is 1Ω1 \Omega.
    Using Ohm's Law V=IRV = IR:

    I=V4R4=3 V1Ω=3 AI = \frac{V_4}{R_4} = \frac{3 \text{ V}}{1 \Omega} = 3 \text{ A}

    This is the total current flowing through the series part of the circuit.

  3. Calculate the voltage across the parallel combination.

    The total voltage supplied by the cells is 4.5 V4.5 \text{ V}.
    The voltage drop across the 1Ω1 \Omega resistor is V4=3 VV_4 = 3 \text{ V}.
    The voltage across the parallel combination (V1V_1 and V2V_2) is the total voltage minus the voltage drop across R4R_4.

    Vparallel=V5−V4=4.5 V−3 V=1.5 VV_{\text{parallel}} = V_5 - V_4 = 4.5 \text{ V} - 3 \text{ V} = 1.5 \text{ V}

    Since V1V_1 measures the voltage across the 2Ω2 \Omega resistor, which is part of the parallel combination, and voltage across parallel components is the same:

    V1=Vparallel=1.5 VV_1 = V_{\text{parallel}} = 1.5 \text{ V}

    The reading on V1V_1 is 1.5 V\boxed{1.5 \text{ V}}.

Part iii

3 A3 \text{ A}

Calculate the reading on A?

  1. Identify ammeter A.

    Ammeter A is in the main circuit, measuring the total current.

  2. Use the current calculated in part (ii).

    The current flowing through the 1Ω1 \Omega resistor (under V4V_4) is the total current in the circuit because it is in series with the parallel combination.

    Itotal=V4R4=3 V1Ω=3 AI_{\text{total}} = \frac{V_4}{R_4} = \frac{3 \text{ V}}{1 \Omega} = 3 \text{ A}

    The reading on A is 3 A\boxed{3 \text{ A}}.

Part iv

6Ω6 \Omega

Calculate the resistance of the unknown resistor?

  1. Use the given combined parallel resistance.

    The combined parallel resistance is 1.5Ω1.5 \Omega. Let the unknown resistor be RxR_x.
    The 2Ω2 \Omega resistor is in parallel with RxR_x.
    The formula for two parallel resistors is:

    1Rparallel=1R1+1Rx\frac{1}{R_{\text{parallel}}} = \frac{1}{R_1} + \frac{1}{R_x}
  2. Substitute known values and solve for RxR_x.

    11.5Ω=12Ω+1Rx\frac{1}{1.5 \Omega} = \frac{1}{2 \Omega} + \frac{1}{R_x} 1Rx=11.5Ω−12Ω\frac{1}{R_x} = \frac{1}{1.5 \Omega} - \frac{1}{2 \Omega} 1Rx=23Ω−12Ω\frac{1}{R_x} = \frac{2}{3 \Omega} - \frac{1}{2 \Omega} 1Rx=46Ω−36Ω\frac{1}{R_x} = \frac{4}{6 \Omega} - \frac{3}{6 \Omega} 1Rx=16Ω\frac{1}{R_x} = \frac{1}{6 \Omega} Rx=6ΩR_x = 6 \Omega

    The resistance of the unknown resistor is 6Ω\boxed{6 \Omega}.

Part v

6 C6 \text{ C}

Calculate the amount of charge that flows through the ammeter in 2 seconds.

  1. Recall the relationship between current, charge, and time.

    Current II is the rate of flow of charge QQ over time tt:

    I=QtI = \frac{Q}{t}
  2. Use the total current from part (iii) and the given time.

    The current through the ammeter is I=3 AI = 3 \text{ A}.
    The time is t=2 st = 2 \text{ s}.

    Q=I×tQ = I \times t Q=3 A×2 sQ = 3 \text{ A} \times 2 \text{ s} Q=6 CQ = 6 \text{ C}

    The amount of charge that flows through the ammeter in 2 seconds is 6 C\boxed{6 \text{ C}}.

Part vi

18 J18 \text{ J}

The resistor under V4V_4 becomes hot. This is due to energy transferred in the resistor. Calculate the amount of energy transferred in the resistor?

  1. Identify the resistor and relevant values.

    The resistor under V4V_4 has a resistance R4=1ΩR_4 = 1 \Omega.
    The voltage across it is V4=3 VV_4 = 3 \text{ V}.
    The current through it is I=3 AI = 3 \text{ A} (from part ii).
    The time is not specified for this part, but typically for energy transfer questions related to heating, a time duration is needed. Assuming the question refers to the same time duration as part (v), which is t=2 st = 2 \text{ s}.

  2. Calculate the energy transferred.

    The energy transferred (heat) EE can be calculated using the formula:

    E=VItE = VIt

    or

    E=I2RtE = I^2Rt

    or

    E=V2RtE = \frac{V^2}{R}t

    Using V4=3 VV_4 = 3 \text{ V}, I=3 AI = 3 \text{ A}, and t=2 st = 2 \text{ s}:

    E=3 V×3 A×2 sE = 3 \text{ V} \times 3 \text{ A} \times 2 \text{ s} E=18 JE = 18 \text{ J}

    The amount of energy transferred in the resistor is 18 J\boxed{18 \text{ J}}.

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