Answer :
Given:
The resistance of the electric blanket, R_b=14.1 Ω
The resistance of the tv, R_t=26.1 Ω
The resistance of the light bulb, R_l=34.5 Ω
The supply voltage, V=113 V
To find:
a. Equivalent resistance of the circuit.
b. The total current in the circuit.
c. The current through the electric blanket.
Explanation:
a. The equivalent resistance of the resistors that are connected in parallel is given by,
[tex]R_{eq}=\frac{R_bR_tR_l}{R_bR_t+R_bR_l+R_tR_l}[/tex]On substituting the known values,
[tex]\begin{gathered} R_{eq}=\frac{14.1\times26.1\times34.5}{14.1\times26.1+14.1\times34.5+26.1\times34.5} \\ =7.20\text{ }\Omega \end{gathered}[/tex]b.
From Ohm's law, the potential difference in the circuit is given by,
[tex]V=IR_{eq}[/tex]Where I is the total current in the circuit.
On substituting the known values,
[tex]\begin{gathered} 113=I\times7.2 \\ \implies I=\frac{113}{7.2} \\ =15.7\text{ A} \end{gathered}[/tex]c.
As the electric blanket is connected in parallel, the potential difference across it is V.
Thus, from Ohm's law,
[tex]V=I__bR_b[/tex]On substituting the known values,
[tex]\begin{gathered} 113=I_b\times14.1 \\ \implies I_b=\frac{113}{14.1} \\ =8.01\text{ A} \end{gathered}[/tex]Final answer:
a. The equivalent resistance of the circuit is 7.20 Ω
b. The total current in the circuit is 15.7 A
c. The current through the electric blanket is 8.01 A