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Zorluk: OrtaSeries Circuits

A 36 V36\text{ V} DC power supply is connected across a series circuit containing a fixed 16 Ω16\ \Omega resistor and a variable rheostat. If an in-line ammeter measures a circuit current of 1.5 A1.5\text{ A}, what is the resistance setting of the rheostat?

  1. A
    24 Ω24\ \Omega
  2. 8 Ω8\ \OmegaCevap
  3. C
    54 Ω54\ \Omega
  4. D
    9.6 Ω9.6\ \Omega

Cevap

8 Ω8\ \Omega
In a series circuit, the current is identical at all points. Applying Ohm's Law gives the total resistance: RT=VTI=36 V1.5 A=24 ΩR_T = \frac{V_T}{I} = \frac{36\text{ V}}{1.5\text{ A}} = 24\ \Omega. Since resistances in series add together linearly (RT=Rfixed+RrheostatR_T = R_{\text{fixed}} + R_{\text{rheostat}}), the rheostat resistance is 24 Ω−16 Ω=8 Ω24\ \Omega - 16\ \Omega = 8\ \Omega.

Adım Adım Çözüm

1
Calculate the total circuit resistance (RTR_T) using Ohm's Law.
RT=VTI=36 V1.5 A=24 ΩR_T = \frac{V_T}{I} = \frac{36\text{ V}}{1.5\text{ A}} = 24\ \Omega
The current in a series circuit is uniform throughout the entire loop, allowing Ohm's Law to determine total loop resistance from total voltage and current.
2
Subtract the fixed resistance from the total series resistance to solve for the unknown rheostat resistance (RrheostatR_{\text{rheostat}}).
Rrheostat=RT−Rfixed=24 Ω−16 Ω=8 ΩR_{\text{rheostat}} = R_T - R_{\text{fixed}} = 24\ \Omega - 16\ \Omega = 8\ \Omega
In a series circuit, total resistance equals the sum of all individual resistances (RT=R1+R2R_T = R_1 + R_2).

Anahtar Kavram

Series Total Resistance and Ohm's Law
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Series Circuits

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