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A moving coil galvanometer with an internal resistance of 5 Ω has a full scale deflection when a current of 20 mA passes through it. Calculate the value of a resistor that will enable it to read 10 A at full scale deflection.

Physics

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Answer

0.01002 Ω\text{0.01002 } \Omega

Step-by-step solution

4 steps
  1. Identify the given values and convert units.

    Internal resistance of the galvanometer, Rg=5 ΩR_g = 5 \, \Omega.
    Full-scale deflection current of the galvanometer, Ig=20 mA=20×10−3 A=0.02 AI_g = 20 \, \text{mA} = 20 \times 10^{-3} \, \text{A} = 0.02 \, \text{A}.
    Desired full-scale deflection current for the ammeter, I=10 AI = 10 \, \text{A}.

  2. Determine the current that must pass through the shunt resistor.

    To convert a galvanometer into an ammeter, a low resistance (shunt resistor, RshR_{sh}) is connected in parallel with the galvanometer. The total current II splits between the galvanometer (IgI_g) and the shunt (IshI_{sh}).

    I=Ig+IshI = I_g + I_{sh} Ish=I−IgI_{sh} = I - I_g Ish=10 A−0.02 AI_{sh} = 10 \, \text{A} - 0.02 \, \text{A} Ish=9.98 AI_{sh} = 9.98 \, \text{A}
  3. Apply the principle that the voltage across parallel components is equal.

    The voltage across the galvanometer (VgV_g) must be equal to the voltage across the shunt resistor (VshV_{sh}).

    Vg=VshV_g = V_{sh}

    Using Ohm's Law (V=IRV = IR):

    IgRg=IshRshI_g R_g = I_{sh} R_{sh}
  4. Solve for the shunt resistance (RshR_{sh}).

    Rsh=IgRgIshR_{sh} = \frac{I_g R_g}{I_{sh}} Rsh=(0.02 A)(5 Ω)9.98 AR_{sh} = \frac{(0.02 \, \text{A}) (5 \, \Omega)}{9.98 \, \text{A}} Rsh=0.19.98 ΩR_{sh} = \frac{0.1}{9.98} \, \Omega Rsh≈0.01002 ΩR_{sh} \approx 0.01002 \, \Omega

    The value of the resistor (shunt) is 0.01002 Ω\text{0.01002 } \Omega.

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