Question

a) A 150Ω resistor is connected in series to a1kΩ resistor and to a battery of 127V. Find the effective resistance and current in the circuit.

b) A 10Ω resistor is connected in parallel to 32Ω resistor and a voltage source of 24V. Find the effective resistance and total current provided in the circuit. Determine the current in each of the resistors.

Answer 1

Part (a)

For series arrangement of reistors

$R_{eff}=R_1+R_2$

$=150+1000=1150\Omega$

Current in circuit

$\Iota=\frac{e.m.f.\>of voltage\> source}{total\> resistance}$

$=\frac{127}{1150}=0.11A$

Part B

Effective resistance for two resistors in parallel

$R_{eff}=\frac{R_1R_2}{R_1+R_2}=\frac{10×32}{10+32}=7.62\Omega$

Total current

$\Iota_T=\frac{e.m.f\>of\>Voltage \>source}{effective\,resistance}$

$=\frac{24}{7.62}=3.15A$

Current through a resistor in parallel arrangement

$\Iota_R=\frac{pd \>across\> the\> parallel \>arrangement}{Resistance \>of \>the \>resistor}$

$\Iota_{10\Omega}=\frac{24}{10}=2.4A$

$\Iota_{32\Omega}=\frac{24}{32}=0.75A$