(a) Redraw the following circuit to show how an ammeter...

(a) Redraw the following circuit to show how an ammeter would be connected to measure the current through the $1.40 \mathrm{k} \Omega$ resistor. (b) Assuming the ammeter to be ideal, what is its reading? (c) If the ammeter has a resistance of $120 \Omega,$ what is its reading?

Key Concepts

Ammeter Connection in Series

An ammeter is used to measure current and must be connected in series with the circuit element of interest. This ensures that the same current flows through both the element and the ammeter, providing an accurate measurement of the current through that component.

Ideal Versus Non-Ideal Instruments

In circuit analysis, an ideal ammeter is assumed to have zero resistance so that it does not affect the overall circuit operation; however, real ammeters have a small, but finite, resistance which can alter the circuit conditions slightly. Understanding this distinction is critical for accurately interpreting measurements and for analyzing how instrument resistance influences the circuit performance.

Ohm's Law and Total Resistance Calculation

Ohm's Law, which relates voltage, current, and resistance, is fundamental in determining the current flowing through a circuit element. By calculating the total resistance in a circuit and applying Ohm's Law, one can determine the expected current, whether the measuring instrument is ideal or has a non-zero resistance. This concept is essential for analyzing and solving circuit problems involving current measurement.

Transcript

00:02 Hi, in the given problem, first of all, we have to redraw the circuit diagram along with an amometer which should be connected such as to measure the current passing through 1 .40 kilo -oom resistor.

00:26 Here this is the circuit which is having two resistors, having the values of 83 .0.

00:37 Kilo -oom and 16 .0 kilo -oom resistors in series and 14 .1 .40 kilo -oam is in their parallel.

00:56 So in order to measure the current passing through this 1 .40 kilo -oom resistor, we should join an amometer in series with 8, such that the negative terminal of an emeter should be towards the negative terminal of the battery.

01:14 Then there is one more resistor, a small resistor, having a value of just 35 om.

01:23 So this completes the circuit diagram in the first part of the problem.

01:29 The required circuit diagram is as shown in the figure.

01:45 Having an emmeter in series with 1 .40 kilo -on to measure the current passing through it.

01:53 Now, in second part of the problem, we have to find out the reading of an emmeter, considering it to be ideal.

02:03 Ideal means its resistance is zero.

02:06 So for an ideal ammeter, its resistance should be zero.

02:21 So now these two resistors are in series combination, 83 and 16 kilo -oom.

02:29 So first of all, their net resistance in series combination, let it be rs, will be 83 .0 plus 16 .0.

02:40 Which comes out to be 99 .0.

02:45 Kilo -oom.

02:47 Now this series combination is in parallel with 1 .40 kilo -oom.

02:51 So this parallel combination will be given by their product in numerator and their addition in denominator.

03:06 So it comes out to be 1 .38 kilo -oam...

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