Question #289993

A 3-Ω light bulb and a 6-Ω light bulb are connected in series with a 6-volt battery. a) What is the current in each bulb? b) What is the voltage across each bulb? c) What is the power dissipated by each bulb? d) What is the total dissipated by the wire?



1
Expert's answer
2022-01-24T11:13:03-0500

To be given in question

R1=3ΩR2=6ΩV=6VR_1=3\Omega\\R_2=6\Omega\\V=6V

Req=R1+R2=3+6=9ΩR_{eq}=R_1+R_2=3+6=9\Omega

(A)

CurrentCurrent

I=VReq=69=0.66AI=\frac{V}{R_{eq}}=\frac{6}{9}=0.66A

(B)

Voltage

V1=I1R1=0.66×3=1.98VV2=I2R2=0.66×6=3.96VV_1=I_1R_1=0.66\times3=1.98V\\V_2=I_2R_2=0.66\times6=3.96V

(C)


P1=I1V1=0.66×1.98=1.3068WP_1=I_1V_1=0.66\times1.98=1.3068W

P2=I2V2=0.66×3.96=2.6136WP_2=I_2V_2=0.66\times3.96=2.6136W

(D) Total power


P=It×Req=0.66×9=5.94WP=I_{t}\times R_{eq}=0.66\times9=5.94W


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