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Directions: Each of the questions or incomplete statements in this section is followed by four suggested answers. Select the best answer in each case. 1. Choose from the options below an oxide of a group 14 (IV) element that exhibits amphoteric character.

Chemistry

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Part 9

Part 9.1

Explain, in words, the meaning of an emf of 12 V.

An electromotive force (emf) of 12 V means that the battery supplies 12 Joules of electrical energy to every 1 Coulomb of charge that passes through it. This energy is converted from chemical energy within the battery.

Part 9.2· 1 step

Calculate the current that passes through the electrical device.

  1. Use the power formula for the electrical device.

    The power dissipated by the electrical device is given as Pdevice=5 WP_{device} = 5 \text{ W}, and its resistance is Rdevice=5ΩR_{device} = 5 \Omega. The formula for power is P=I2RP = I^2 R.

    Pdevice=Idevice2RdeviceP_{device} = I_{device}^2 R_{device} 5 W=Idevice2(5Ω)5 \text{ W} = I_{device}^2 (5 \Omega) Idevice2=5 W5ΩI_{device}^2 = \frac{5 \text{ W}}{5 \Omega} Idevice2=1 A2I_{device}^2 = 1 \text{ A}^2 Idevice=1 A2I_{device} = \sqrt{1 \text{ A}^2} Idevice=1 AI_{device} = \boxed{\text{1 A}}

Part 9.3· 4 steps

Calculate the resistance of resistor RxR_x.

The total current flowing from the battery is Itotal=Idevice=1 AI_{total} = I_{device} = 1 \text{ A}. The battery has an emf of 12 V12 \text{ V} and an internal resistance r=1Ωr = 1 \Omega.

  1. Calculate the total resistance of the circuit.

    The total resistance RtotalR_{total} is given by Ohm's law for the entire circuit: emf=ItotalRtotal\text{emf} = I_{total} R_{total}.

    Rtotal=emfItotalR_{total} = \frac{\text{emf}}{I_{total}} Rtotal=12 V1 AR_{total} = \frac{12 \text{ V}}{1 \text{ A}} Rtotal=12ΩR_{total} = 12 \Omega

  2. Calculate the total external resistance RextR_{ext}.

    The total resistance is the sum of the external resistance and the internal resistance: Rtotal=Rext+rR_{total} = R_{ext} + r.

    Rext=Rtotal−rR_{ext} = R_{total} - r Rext=12Ω−1ΩR_{ext} = 12 \Omega - 1 \Omega Rext=11ΩR_{ext} = 11 \Omega

  3. Calculate the equivalent resistance of the parallel combination, RparallelR_{parallel}.

    The external circuit consists of the electrical device (Rdevice=5ΩR_{device} = 5 \Omega) in series with a parallel combination of resistors.

    Rext=Rdevice+RparallelR_{ext} = R_{device} + R_{parallel} 11Ω=5Ω+Rparallel11 \Omega = 5 \Omega + R_{parallel} Rparallel=11Ω−5ΩR_{parallel} = 11 \Omega - 5 \Omega Rparallel=6ΩR_{parallel} = 6 \Omega

  4. Use the parallel resistance formula to find RxR_x.

    The parallel combination consists of two branches:
    Branch 1: R1=4Ω+RxR_1 = 4 \Omega + R_x (since switch S is closed).
    Branch 2: $R_2 = 3

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