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Chapter 14: Problem 32

A galvanometer of resistance \(400 \Omega\) can measure a current of \(1 \mathrm{~mA}\). To convert it into a voltmeter of range \(8 \mathrm{~V}\), the required resistance is (A) \(4600 \Omega\) (B) \(5600 \Omega\) (C) \(6600 \Omega\) (D) \(7600 \Omega\)

Short Answer

Expert verified
The required resistance to convert the galvanometer into a voltmeter with a range of 8 V is 7600 惟. Therefore, the correct answer is (D) 7600 惟.

Step by step solution

01

Understand the given information

We know that 1. The resistance of the galvanometer (G) is 400 惟. 2. The maximum current the galvanometer can measure (I) is 1 mA. 3. The range of the voltmeter (V) is 8 V. We need to find the required resistance (R) to convert the galvanometer into a voltmeter.
02

Use Ohm's Law

Ohm's Law states that \(V = IR\), where V is the voltage, I is the current, and R is the resistance. First, let's calculate the galvanometer's total resistance when it is used as a voltmeter. To do this, we can rearrange Ohm's Law to solve for the total resistance: \[R = \frac{V}{I}\] Now, plug in the given values for V (8 V) and I (1 mA or 0.001 A): \[R = \frac{8}{0.001}\]
03

Calculate the total resistance

Calculate R: \[R = 8000 \Omega\] The total resistance needed for the voltmeter is 8000 惟.
04

Find the required resistance

Now, we have to find the required resistance to be added in series with the galvanometer. Since the galvanometer and the required resistance are connected in series, their resistances need to add up to the total resistance. \[R_{req} = R_{total} - R_{galvanometer}\] Plug in the values for the total resistance (8000 惟) and the given resistance of the galvanometer (400 惟): \[R_{req} = 8000 - 400\]
05

Calculate the required resistance

Calculate \(R_{req}\): \[R_{req} = 7600 \Omega\] The required resistance to convert the galvanometer into a voltmeter with a range of 8 V is 7600 惟. Therefore, the correct answer is (D) 7600 惟.

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Most popular questions from this chapter

An energy source will supply a constant current into the load, if its internal resistance is (A) Equal to the resistance of the load. (B) Very large as compared to the load resistance. (C) Zero. (D) Non-zero but less than the resistance of the load.

This question has statement I and statement II. Of the four choices given after the statements, choose the one that best describes the two statements. Statement-I: Higher the range, greater is the resistance of ammeter. Statement-II: To increase the range of ammeter, additional shunt needs to be used across it. (A) Statement-I is true, Statement-II is true, Statement-II is not the correct explanation of Statement-I. (B) Statement-I is true, Statement-II is false. (C) Statement-I is false, Statement-II is true. (D) Statement-I is true, Statement-II is true, Statement-II is correct explanation of Statement-I.

A galvanometer having a coil resistance of \(100 \Omega\) gives a full scale deflection, when a current of \(1 \mathrm{~mA}\) is passed through it. The value of the resistance, which can convert this galvanometer into ammeter giving a full scale deflection for a current of \(10 \mathrm{~A}\), is (A) \(2 \Omega\) (B) \(0.1 \Omega\) (C) \(3 \Omega\) (D) \(0.01 \Omega\)

Figure \(14.47\) shows the circuit of a potentiometer. The length of the potentiometer wire \(A B\) is \(50 \mathrm{~cm}\). The EMF \(E_{1}\) of the battery is \(4 \mathrm{~V}\), having negligible internal resistance. Value of \(R_{1}\) and \(R_{2}\) are \(15 \Omega\) and \(5 \Omega\), respectively. When both the keys are open, the null point is obtained at a distance of \(31.25 \mathrm{~cm}\) from \(A\), but when both the keys are closed, the balance length reduces to \(5 \mathrm{~cm}\) only. Given \(R_{A B}=10 \Omega\) The balance length when key \(K_{1}\) is open and \(K_{2}\) is closed is given by (A) \(10.5 \mathrm{~cm}\) (B) \(11.5 \mathrm{~cm}\) (C) \(12.5 \mathrm{~cm}\) (D) \(25 \mathrm{~cm}\)

The average bulk resistivity of the human body (apart from the surface resistance of the skin) is about \(5 \Omega m\). The conducting path between the hands can be represented approximately as a cylinder \(1.6 \mathrm{~m}\) long and \(0.1 \mathrm{~m}\) diameter. The skin resistance may be made negligible by soaking the hands in salt water. A lethal shock current needed is \(100 \mathrm{~mA}\). Note that a small amount of potential difference could be fatal if the skin is damp. What potential difference is needed between the hands for a lethal shock current? (A) \(100 \mathrm{~V}\) (B) \(10 \mathrm{~V}\) (C) \(120 \mathrm{~V}\) (D) \(150 \mathrm{~V}\)
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