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Question 24.10: In Fig. 24.15, let R1 = 6 Ω, R2 = 3 Ω, and ΔV = 18 V. Find t......

In Fig. 24.15, let R_{1}  =  6  Ω,  R_{2} = 3 Ω, and ΔV = 18 V. Find the three currents I, I_{1},  and  I_{2} in the circuit.

fig 24.15
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The equivalent resistance of the parallel combination is:

{\frac{1}{R_{\mathrm{eq}}}}={\frac{1}{R_{1}}}+{\frac{1}{R_{2}}}={\frac{1}{6\,\Omega}}+{\frac{1}{3\,\Omega}}={\frac{1}{2\,\Omega}}

Then :           R_{\mathrm{eq}}=2\,\Omega

Now we calculate the three currents in the circuit as follows:

I={\frac{\Delta V}{R_{\mathrm{eq}}}}={\frac{18\,\mathrm{V}}{2\,\Omega}}=9\,\mathrm{A}\ \ I_{1}={\frac{\Delta V}{R_{1}}}={\frac{18\,\mathrm{V}}{6\,\Omega}}=3\,\mathrm{A}\ \ I_{2}={\frac{\Delta V}{R_{2}}}={\frac{18\,\mathrm{V}}{3\,\Omega}}=6\,\mathrm{A}

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