• :00Days
  • :00Hours
  • :00Mins
  • 00Seconds
A new era for learning is coming soonSign up for free
Log In Start studying!

Select your language

Suggested languages for you:
Answers without the blur. Sign up and see all textbooks for free! Illustration

52P

Expert-verified
Fundamentals Of Physics
Found in: Page 798

Answers without the blur.

Just sign up for free and you're in.

Illustration

Short Answer

A simple ohmmeter is made by connecting a 1.50 V flashlight battery in series with a resistance R and an ammeter that reads from 0 to 1.00 mA, as shown in Fig. 27-59. Resistance R is adjusted so that when the clip leads are shorted together, the meter deflects to its full-scale value of 1.00 mA. What external resistance across the leads results in a deflection of (a) 10.0%, (b) 50.0%, and (c) 90.0%of full scale? (d) If the ammeter has a resistance of 20.0 Ωand the internal resistance of the battery is negligible, what is the value of R?

  1. The external resistance that results across the leads results in a deflection of 10% is 1.35×104 Ω.
  2. The external resistance that results across the leads results in a deflection of 50% is 1.5×103 Ω.
  3. The external resistance that results across the leads results in a deflection of 90.0% full scale is 167 Ω.
  4. The value of R is 1.48×103 Ω.
See the step by step solution

Step by Step Solution

Step 1: The given data

The voltage of the flashlight battery, V=1.50 V

Ammeter reads from 0mA to 1.00 mA

Deflection of ammeter after adjustments of the resistance, i=1.00 mA

Resistance of ammeter, R=20 Ω

Step 2: Understanding the concept of resistance

In a given figure, we need to check the resistance combination of the circuit, to gain a clear idea of the equivalent resistance due to the contribution of every resistance present in the circuit. Now, using Ohm's law in the given situation, we can solve for the maximum and variable current case to get the required resistances for each case.

Formulae:

The voltage equation using Ohm’s law, V=IR (1)

The equivalent resistance for a series combination of the resistors, Req=inRi (2)

Step 3: a) Calculation of the external resistance for deflection 10%

From the given combination, the current flowing through the circuit can be given using equation (2) in equation (1) as follows:

i=εR+Rexti=RimaxR+Rext imax=εRRext=Rimaxi1........................(3)

Now, the internal resistance can be given using equation (1) as follows:

" width="9" height="19" role="math" style="max-width: none; vertical-align: -4px;" localid="1664352318254">" width="9" height="19" role="math" style="max-width: none; vertical-align: -4px;" localid="1664352323339">

R=εimax=1.50 V1.00×103A=1.50×103 Ω

Thus, the external resistance value for the current value getting 10% deflection is given using the given data in equation (3) as follows:

Rext=1.50×103 Ω10.101=1.35×104 Ω

Hence, the value of the external resistance is 1.35×104 Ω.

Step 4: b) Calculation of the external resistance for deflection 50%

The external resistance value for the current value getting 50% deflection is given using the given data in equation (3) as follows:

Rext=1.50×103 Ω10.501=1.5×103 Ω

Hence, the value of the external resistance is 1.5×103 Ω .

Step 5: c) Calculation of the external resistance for deflection 90%

The external resistance value for the current value getting 90% deflection is given using the given data in equation (a) as follows:

Rext=1.50×103 Ω10.901=167 Ω

Hence, the value of the external resistance is 167 Ω.

Step 6: d) Calculation of the value of R

With the ammeter having a resistance value, the total internal resistance using equation (2) for the given circuit becomes:

r=RA+R (where, r is the resitance of the flashlight battery)R=rRAR=εimaxRAR=1.50 V1.00×103 A20 ΩR=1500 Ω20 ΩR=1.48×103 Ω

Hence, the value of the unknown resistance for the given ammeter reading is 1.48×103 Ω.

Recommended explanations on Physics Textbooks

94% of StudySmarter users get better grades.

Sign up for free
94% of StudySmarter users get better grades.