Explanation:
(1). Given that,
Resistance [tex]R = 15.0\times10^{3}\Omega[/tex]
Voltage [tex]V = 45.0\ V[/tex]
Using ohm's law
[tex]V = I\times R[/tex]
(a). Draw a circuit
(b).The current is defined as:
[tex]I = \dfrac{V}{R}[/tex].....(I)
Here, V = voltage
R = resistance
I = current
Put the value of V and R in equation (I)
[tex]I=\dfrac{45.0}{15.0\times10^{3}}[/tex]
[tex]I=0.003\ A[/tex]
The current is 0.003 A.
(c). The power dissipated by the resistor will be
[tex]P=\dfrac{V^2}{R}[/tex]
[tex]P = \dfrac{(45.0)^2}{15000}[/tex]
[tex]P = 0.135\ \ W[/tex]
The power dissipated by the resistor will be 0.135 Watt.
(2). Given that,
Resistance [tex]R_{1} = 10.0 \Omega[/tex]
Resistance [tex]R_{2} = 8.0 \Omega[/tex]
Resistance [tex]R_{3} = 27.0 \Omega[/tex]
Voltage [tex]V = 9.0\ \ V[/tex]
(a). Draw a circuit
(b). The equivalent circuit will be
[tex]R_{eq}=R_{1}+R_{2}+R_{3}[/tex]
[tex]R_{eq}=10+8+27[/tex]
[tex]R_{eq}=45\ \Omega[/tex]
The current is defined as:
[tex]I = \dfrac{V}{R}[/tex].....(I)
Here, V = voltage
R = resistance
I = current
Put the value of V and R in equation (I)
[tex]I=\dfrac{9.0}{45.0}[/tex]
[tex]I=0.2\ A[/tex]
The current is 0.2 A.
(c). The voltage drop across each resistor in the circuit
The voltage drop across 10.0 ohm resistor,
[tex]V = I\times R[/tex]
[tex]V = 0.2\times 10[/tex]
[tex]V = 2\ \ volt[/tex]
The voltage drop across 8.0 ohm resistor,
[tex]V = I\times R[/tex]
[tex]V = 0.2\times 8.0[/tex]
[tex]V = 1.6\ \ volt[/tex]
The voltage drop across 27.0 ohm resistor,
[tex]V = I\times R[/tex]
[tex]V = 0.2\times 27.0[/tex]
[tex]V = 5.4\ \ volt[/tex]
The voltage drop across each resistor in the circuit is 2 V, 1.6 V and 5.4 V.
(3). Given that,
Resistance [tex]R_{1} = 2.0 \Omega[/tex]
Resistance [tex]R_{2} = 5.0 \Omega[/tex]
Resistance [tex]R_{3} = 10.0 \Omega[/tex]
Voltage [tex]V = 12.0\ V[/tex]
(a). Draw a circuit
(b). The equivalent resistance will be
[tex]\dfrac{1}{R_{eq}}=\dfrac{1}{R_{1}}+\dfrac{1}{R_{2}}+\dfrac{1}{R_{3}}[/tex]
[tex]\dfrac{1}{R_{eq}}=\dfrac{1}{2.0}+\dfrac{1}{5.0}+\dfrac{1}{10.0}[/tex]
[tex]\dfrac{1}{R_{eq}}=\dfrac{4}{5}[/tex]
[tex]R_{eq}=1.25\ \Omega[/tex]
The equivalent resistance will be 1.25 ohm.
(c). The current passing through each resistor in the circuit.
The current passing through 2.0 ohm resistor
[tex]I = \dfrac{V}{R_{1}}[/tex]
[tex]I=\dfrac{12.0}{2.0}[/tex]
[tex]I = 6\ A[/tex]
The current passing through 5.0 ohm resistor
[tex]I = \dfrac{V}{R_{1}}[/tex]
[tex]I=\dfrac{12.0}{5.0}[/tex]
[tex]I = 2.4\ A[/tex]
The current passing through 10.0 ohm resistor
[tex]I = \dfrac{V}{R_{1}}[/tex]
[tex]I=\dfrac{12.0}{10.0}[/tex]
[tex]I = 1.2\ A[/tex]
The current passing through each resistor in the circuit is 6 A, 2.4 A and 1.2 A.
