Conversion to Ammeter and Voltmeter - UNSOLVED PRACTICE SET

Q7. Derive the expression for the shunt resistance required to convert a galvanometer into an ammeter of given range.

Q8. Derive the expression for the series resistance required to convert a galvanometer into a voltmeter of given range.

Q9. A galvanometer has resistance 50 Ω and full-scale deflection current 1 mA. Calculate the shunt resistance needed to convert it into an ammeter of range 0–5 A.

Q10. Why should an ammeter have very low resistance? What would happen if it had high resistance?

Q11. Why should a voltmeter have very high resistance? What would happen if it had low resistance?

Q12. A galvanometer of resistance 100 Ω shows full-scale deflection at 2 mA. Calculate the series resistance needed to convert it into a voltmeter of range 0–10 V.

Q13. Explain with a circuit diagram how a galvanometer is converted into an ammeter. Derive the expression for the shunt resistance. Why must the shunt resistance be very small compared to the galvanometer resistance?

Q14. Explain with a circuit diagram how a galvanometer is converted into a voltmeter. Derive the expression for the series resistance. Why must the series resistance be very large compared to the galvanometer resistance?

Q15. A galvanometer has coil resistance G = 80 Ω and full-scale deflection current I_g = 0.5 mA.

(a) Calculate the shunt resistance to convert it into an ammeter of range 0–2 A.  

(b) Calculate the series resistance to convert it into a voltmeter of range 0–20 V.  

(c) Calculate the effective resistance of the converted ammeter and voltmeter.  

(d) If this ammeter is connected in series with a 10 Ω resistor across a 5 V battery, what current does it show?  

(e) If the voltmeter is connected across the same 10 Ω resistor, what voltage does it show?

Q16. In a school electronics club, students are building measurement instruments from a salvaged galvanometer. The galvanometer has G = 120 Ω and I_g = 100 μA.

(a) They want to build an ammeter with ranges 0–1 mA, 0–10 mA, and 0–100 mA using an Ayrton shunt. Design the shunt circuit and calculate all resistances.  

(b) They also want to build a voltmeter with ranges 0–1 V, 0–10 V, and 0–100 V using a multiplier circuit. Calculate the series resistances for each range.  

(c) Calculate the effective resistance of the ammeter (at 100 mA range) and the voltmeter (at 100 V range).  

(d) A student accidentally connects the ammeter (100 mA range) directly across a 9 V battery. What happens? Calculate the current through the galvanometer.  

(e) Explain why the ammeter and voltmeter must always be connected correctly (ammeter in series, voltmeter in parallel) in a circuit.

Q17. A multimeter is designed using a galvanometer with G = 50 Ω and I_g = 1 mA. The multimeter has the following ranges:

- DC Current: 0–10 mA, 0–100 mA, 0–1 A

- DC Voltage: 0–1 V, 0–10 V, 0–100 V

- Resistance: ×1, ×10, ×100, ×1k

(a) Calculate the shunt resistances for all current ranges.  

(b) Calculate the series resistances for all voltage ranges.  

(c) For the resistance measurement, a 1.5 V battery is used. Calculate the series resistance for the ×100 range (center scale = 15 Ω).  

(d) If the multimeter is set to the 10 V DC range and connected across a resistor carrying 50 mA, what reading does it show?  

(e) Explain why the ohmmeter scale is non-linear (reversed and compressed at one end).

Q18. In a physics experiment, a student needs to measure the current through and voltage across a resistor R = 5 Ω connected to a battery of EMF 3 V with internal resistance r = 0.5 Ω.

(a) Calculate the true current and true voltage across R.  

(b) The student uses an ammeter of resistance R_A = 0.1 Ω and a voltmeter of resistance R_V = 1000 Ω. Draw two possible circuit configurations: (i) ammeter before voltmeter, and (ii) voltmeter before ammeter.  

(c) For configuration (i), calculate the measured current and voltage, and the percentage error in each.  

(d) For configuration (ii), calculate the measured current and voltage, and the percentage error in each.  

(e) Which configuration is better for this measurement? Explain the general rule for choosing the correct configuration based on the relative magnitudes of R, R_A, and R_V.