Solving Resistor Circuits Practice Problems

An experimental circuit is shown below. All meters and batteries are ideal. When the 18.0 Ω resistor is plucked out (creating a gap), the voltmeter displays 12.0 V. Determine the ammeter reading when the 18.0 Ω is replaced with a low resistance shunt. 

Determine the discharge time constant of the capacitors shown in the figure provided.

How much time does it take for the charge on the capacitor in an RC circuit with a time constant of 20 ms to i) decrease to one-fourth of its initial value? ii) Additionally, after the discharge begins, how long does it take for the energy stored in the capacitor to decrease to 75% of its initial value?

Consider a 200 μF capacitor charged to an initial voltage of 1800 V. If it loses 85% of its charge within 25 ms when discharged through a certain component, determine the resistance of this component.

In a specific circuit arrangement, a 25 μF capacitor initially charged to 10 V is linked in parallel with a resistor. As the capacitor gradually discharges, its stored energy decreases by 60% within a time span of 0.3 s. Determine the resistance value required for this circuit.

Consider the following circuit configuration. Find an expression for the current i, as a function of time 't'.

As a part of the competition, you are provided with 2.0 g of copper and tasked with creating a wire that can dissipate 10.0 W of power when connected to a 2.0 V power source. Calculate the length and diameter of the copper wire to meet this requirement. The resistivity of copper is 1.7 × 10^-8 Ω-m and the density of copper is 8.94 × 10³ kg/m³.

A pair of metal pieces, both measuring 8 cm × 8 cm, are positioned 0.5 cm apart. One of the pieces has a +15 nC charge while the other is charged to -7.5 nC. The two metal pieces are connected to each other by a metallic string. Will the electric current through the circuit exhibit a tendency to increase, decrease, or remain constant over time? 

Following the initial charging of a 200 μF capacitor to 12 V, it is connected in parallel with a 3000 Ω resistor. The capacitor discharges through the resistor, although at a slower rate compared to a direct wire connection of the plates. If the fully charged capacitor is connected to the resistor at t = 0 s, determine the time at which the capacitor voltage decreases by a quarter to reach 9.0 V.

A 3-A current passes through a cylindrical conductor with a radius of 4 mm. The current density in the conductor, which varies along the radial direction, is defined by J = Jₑ(r/R)², where Jₑ is the current density at its surface. What is the value of Jₑ?

Determine the current that would flow through a 3.0-meter-long wire with a radius of 0.25 mm, which has a resistivity described by the equation ρ(x) = (3.0 × 10^-7 Ω•m) + (4.0 × 10^-7 Ω)x, when it is connected to a 12.0 V battery.

Consider an electric circuit where the amount of charge flowing through a wire over time t is given by the function Q(t) = 2sin(t) + 3t, where t represents time in seconds. Express the current in the wire as a function of time.

The amount of charge flowing through a conductor over time is given by the function Q(t) = 5t  ² - 3t, where t is in seconds, and Q cannot exceed a maximum value of 10 coulombs. Plot a graph of the current (I) versus time (t) over the interval t in which the amount of Q is allowed.

A capacitor is being charged through a resistor in an electric circuit. The total charge that has entered the capacitor at time t is given by the equation Q = (10 μC) (1 - e^{(-t/5 s)}), where t is the time in seconds. What is the maximum value of the current flowing through the resistor?

A capacitor is being discharged through a resistor in an electric circuit. The current flowing through the resistor decreases over time as the capacitor discharges. The current as a function of time is given by the equation I = (2 A)e^{-t/5 s}, where t represents time in seconds since the discharging process started. Determine the total charge that has flowed out of the capacitor from the initial time until the current becomes zero.

Determine the unknown resistance R_a in the electric circuit shown below. 

Consider the electronic circuit shown in the figure below. The circuit comprises two unknown resistors, denoted as R_x, and a third resistor with a known value of 50 Ω. The equivalent resistance between points A and B is measured to be 18.75 Ω. Determine the value of R_x.

A capacitor of 15 μF capacitor is discharged through an unknown resistor. The current flowing through the resistor is measured using an ammeter. The recorded data is presented in the table below. Determine:

i) the resistance

ii) the initial voltage across the capacitor.

A 1.5-V AA battery is powering a small LED light with a resistance of 5 Ω. When the LED light is on, the voltage across the battery terminals is measured to be 1.3 V. Calculate the internal resistance of the battery.

To minimize power dissipation in the circuit shown, which specific pair of points should a 9 V battery be connected to?

A solar-powered device uses two 12.0 V batteries connected in series. The resistance of the device is 22.0 Ω. The power supplied to the device decreases as the battery power gets depleted due to increased internal resistance. Assuming zero initial resistance, determine the total internal resistance from both batteries when the power supplied by the batteries to the device is a quarter of the initial value.

In the circuit below, find the current through the 4-Ω resistor.

Imagine working in a physics lab with a galvanometer with a sensitivity of 30 kΩ/V and an internal resistance of 15 Ω. Your task is to modify this galvanometer to function as an ammeter capable of reading up to 2.0 A at full scale. How would you achieve the desired output?

You have a galvanometer with an internal resistance of 40 Ω that shows full-scale deflection with a 60 μA current. You need to modify this galvanometer to function as a voltmeter that measures up to 300 V. How can you achieve the desired results?

You are in a physics lab working with a milliammeter with a full-scale reading of 50 mA. It contains a 0.10-ohm resistor in parallel with a 50-ohm galvanometer. You now need to use this instrument to measure voltage, with a full-scale reading of 50 V, and you cannot disassemble the ammeter. How would you modify it to serve as a voltmeter, and what would be its sensitivity in ohms per volt?

A strain gauge sensor is affixed to a metal rod to measure small changes in its length. The sensor has an initial length of L₀, a cross-sectional area of A₀, and a resistance of R₀. As the rod deforms, the sensor's length changes by ΔL, and the resistance changes by ΔR. Assuming that the volume of the sensor remains constant, derive an expression approximating the strain: $\frac{\Delta L}{L_0}$ , in terms of ΔR and R₀.

A dielectric material with resistivity of "ρ" and dielectric constant of "K" is placed between the plates of a parallel-plate capacitor. The capacitor, which is disconnected from a battery, has charges of +Q and -Q on these plates. Modeling the system with the dielectric as a resistor in parallel with the capacitor, determine the time constant "τ" for discharge if the dielectric is rubber with 𝜌 = 2.0×10¹³ Ω⋅m and K = 3.0.

A 2.0 μF capacitor is to be charged to 2500 V in 3.0 seconds. Assume that this 2500 V is 90% of the full source voltage. Determine the resistance that is required.

If two LEDs are connected to a 200 V DC source in series, they will consume a quarter of the power source compared to the condition when they are connected in parallel instead. Given that the resistance of one of the LEDs is 3.9 kΩ, calculate the resistance of the other LED. Assume that the internal resistance of the DC source is zero.

Two light bulbs are connected in series with a 12.5-V power supply. The first bulb has a resistance of 10 kΩ. A voltmeter with 18.5 kΩ internal resistance measures 4.2 V across the second bulb. What is the resistance of the second bulb?

A 12.0 m cable consists of 6.0 m of Fe followed by 6.0 m of Ni, both with a diameter of 1.6 mm. Across the entire length of the cable, a potential difference of 120 mV is applied. What is i. the total resistance of the cable, ii. the current flowing through the cable, and iii. the voltage across the Ni and Fe sections of the cable? Hint: Use the following resistivities: Ni = 6.84 × 10 ^-8 Ω·m, Fe = 9.71 × 10^-8 Ω·m.