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A circuit contains a 6V battery with internal resistance 2 ohms. Resistors P=10 ohms, Q=10 ohms, and R=15 ohms are connected as follows: P and R are in parallel, and this combination is in series with

Physics

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Answer

0.33 A\text{0.33 A}

DECREASE\text{DECREASE}

INCREASE\text{INCREASE}

Step-by-step solution

8 steps

Here's the solution to your circuit problem:

11.2.1

To calculate the ammeter reading when switch S is closed, we first find the total resistance of the circuit.

  1. Calculate the equivalent resistance of resistors P and R, which are connected in parallel.

    RPR=RP×RRRP+RRR_{PR} = \frac{R_P \times R_R}{R_P + R_R} RPR=10 Ω×15 Ω10 Ω+15 ΩR_{PR} = \frac{10 \, \Omega \times 15 \, \Omega}{10 \, \Omega + 15 \, \Omega} RPR=150 Ω225 Ω=6 ΩR_{PR} = \frac{150 \, \Omega^2}{25 \, \Omega} = 6 \, \Omega
  2. Calculate the total external resistance (RextR_{ext}).

    Resistor Q is in series with the parallel combination of P and R.

    Rext=RPR+RQR_{ext} = R_{PR} + R_Q Rext=6 Ω+10 Ω=16 ΩR_{ext} = 6 \, \Omega + 10 \, \Omega = 16 \, \Omega
  3. Calculate the total resistance of the circuit (RtotalR_{total}), including the internal resistance (rr).

    Rtotal=Rext+rR_{total} = R_{ext} + r Rtotal=16 Ω+2 Ω=18 ΩR_{total} = 16 \, \Omega + 2 \, \Omega = 18 \, \Omega
  4. Calculate the total current (ItotalI_{total}) using Ohm's law for the entire circuit.

    This is the ammeter reading.

    Itotal=ERtotalI_{total} = \frac{\mathcal{E}}{R_{total}} Itotal=6 V18 Ω=13 AI_{total} = \frac{6 \, \text{V}}{18 \, \Omega} = \frac{1}{3} \, \text{A}

    The ammeter reading is 0.33 A\boxed{\text{0.33 A}}.

    11.2.2

    The switch S is now open.

  5. When switch S is opened, resistor R (15 Ω\Omega) is removed from the circuit.

    The external circuit now consists only of resistor P (10 Ω\Omega) in series with resistor Q (10 Ω\Omega).
    The new total external resistance (Rext′R'_{ext}) is:

    Rext′=RP+RQ=10 Ω+10 Ω=20 ΩR'_{ext} = R_P + R_Q = 10 \, \Omega + 10 \, \Omega = 20 \, \Omega

    The new total resistance of the circuit (Rtotal′R'_{total}) is:

    Rtotal′=Rext′+r=20 Ω+2 Ω=22 ΩR'_{total} = R'_{ext} + r = 20 \, \Omega + 2 \, \Omega = 22 \, \Omega
  6. Compare the new total resistance (22 Ω22 \, \Omega) with the previous total resistance (18 Ω18 \, \Omega).

    The total resistance has increased.

  7. According to Ohm's law (I=ERtotalI = \frac{\mathcal{E}}{R_{total}}), if the total resistance increases while the EMF remains constant, the total current will decrease.

    The new total current (Itotal′I'_{total}) would be:

    Itotal′=6 V22 Ω=311 A≈0.27 AI'_{total} = \frac{6 \, \text{V}}{22 \, \Omega} = \frac{3}{11} \, \text{A} \approx 0.27 \, \text{A}

    Since 0.27 A<0.33 A0.27 \, \text{A} < 0.33 \, \text{A}, the ammeter reading will DECREASE.

  8. Reason

    When switch S is opened, resistor R is removed from the parallel branch. This increases the total external resistance of the circuit. According to Ohm's law, an increase in total resistance leads to a decrease in the total current flowing through the circuit.
    The ammeter reading will DECREASE\boxed{\text{DECREASE}}.

    11.2.3

    The voltmeter measures the terminal potential difference (Vterminal=E−IrV_{terminal} = \mathcal{E} - Ir).
    From 11.2.2, we determined that when switch S is opened, the total current (II) in the circuit decreases.
    Since the EMF (E\mathcal{E}) and internal resistance (rr) are constant, a decrease in II means that the voltage drop across the internal resistance (IrIr) will decrease.
    Therefore, Vterminal=E−IrV_{terminal} = \mathcal{E} - Ir will increase because a smaller value is subtracted from the constant EMF.
    The voltmeter reading will INCREASE\boxed{\text{INCREASE}}.

    11.2.4

    The voltmeter measures the terminal potential difference, which is given by the formula Vterminal=E−IrV_{terminal} = \mathcal{E} - Ir. When switch S is opened, the total external resistance of the circuit increases, causing the total current (II) to decrease. Since the internal resistance (rr) is constant, a decrease in the total current (II) results in a smaller voltage drop (IrIr) across the internal resistance. Consequently, the terminal potential difference (VterminalV_{terminal}) increases because a smaller amount is subtracted from the constant EMF (E\mathcal{E}).

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