Chapter 1

The equivalent circuit is shown in figure Alla, which reduces to that of figure Al.lb since the 8 Ω and 1 kΩ are in parallel and by the product-over-sum rule these combine to give a resistance of <m:math display='block'> <m:semantics> <m:mrow> <m:mi>R</m:mi><m:mo>=</m:mo><m:mfrac> <m:mrow> <m:mn>8</m:mn><m:mo>*</m:mo><m:mn>1000</m:mn></m:mrow> <m:mrow> <m:mn>8</m:mn><m:mo>+</m:mo><m:mn>1000</m:mn></m:mrow> </m:mfrac> <m:mo>=</m:mo><m:mfrac> <m:mrow> <m:mn>8000</m:mn></m:mrow> <m:mrow> <m:mn>1008</m:mn></m:mrow> </m:mfrac> <m:mo>=</m:mo><m:mn>7.9365</m:mn><m:mi>&#x03A9;</m:mi></m:mrow> <m:annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOuaiabg2 da9maalaaabaGaaGioaiaacQcacaaIXaGaaGimaiaaicdacaaIWaaa baGaaGioaiabgUcaRiaaigdacaaIWaGaaGimaiaaicdaaaGaeyypa0 ZaaSaaaeaacaaI4aGaaGimaiaaicdacaaIWaaabaGaaGymaiaaicda caaIWaGaaGioaaaacqGH9aqpcaaI3aGaaiOlaiaaiMdacaaIZaGaaG OnaiaaiwdacqqHPoWvaaa@4EC6@ </m:annotation> </m:semantics> </m:math> ]]</Eq uationSource><EquationSource Format="TEX"><![CDATA[$$R = \frac{{8*1000}}{{8 + 1000}} = \frac{{8000}}{{1008}} = 7.9365\Omega \$$ Then the total series resistance is 2 + 0.1 + 7.9365 = 10.0365 Ω and the current, I, is 9/10.0365 = 0.8967 A. Then the voltage across the 7.9365Ω resistance is 0.8967 × 7.9365 = 7.117 V, which is the required voltmeter reading.